Questions Bank-Essay Type-Polynomials - Class X

Question 1 of 52

1. Question

1 point(s)

The graph of \(y=f(x) \) cuts the x-axis at \((1,0) \) and \(\left(\dfrac{-3}{2},0\right) \). Find all the zeroes of \(f(x) \)

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Question 2 of 52

2. Question

1 point(s)

Show that \(1,-1 \) and \(3 \) are the zeroes of the polynomial \(x^3-3x^2-x+3 \).

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Question 3 of 52

3. Question

1 point(s)

Write the polynomial, the product and sum of whose zeroes are \(\dfrac{-9}{2} \) and \(\dfrac{-3}{2} \) respectively

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Question 4 of 52

4. Question

1 point(s)

If \((x+a) \) is a factor of \(2x^2+2ax+5x+10 \), find \( a\).

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Question 5 of 52

5. Question

1 point(s)

If \(\alpha \) and \(\beta \) are the zeroes of the quadratic polynomial \(f(t)=t^2-4t+3 \), find the value of \(\alpha^4\beta^4+\alpha^3\beta^4 \)

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Question 6 of 52

6. Question

1 point(s)

Find a quadratic polynomial, the sum and product of whose zeroes are \(\sqrt2 \) and \(\dfrac{1}{3} \) respectively.

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Question 7 of 52

7. Question

1 point(s)

Divide \(6x^3+13x^2+x-2 \) by \(2x+1 \), and find the quotient and remainder.

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Question 8 of 52

8. Question

1 point(s)

Divide \(x^4-3x^2+4x+5 \) by \(x^2-x+1 \), find quotient and remainder.

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Question 9 of 52

9. Question

1 point(s)

\(\alpha,\beta \) are the roots of the quadratic polynomial \(p(x)=x^2-(k+6)x+2\ (2k-1) \). Find the value of \(k \), if \(\alpha+\beta=\dfrac{1}{2}\alpha\beta \)

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Question 10 of 52

10. Question

1 point(s)

\(\alpha,\beta \) are the roots of the quadratic polynomial \(p(x)=x^2-(k+6)x+2\ (2k-1) \). Find the value of \(k \), if \(\alpha+\beta=\dfrac{1}{2}\alpha\beta \)

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Question 11 of 52

11. Question

1 point(s)

What must be added to polynomial \(f(x)=x^4+2x^3-2x^2+x-1 \) so that the resulting polynomial is exactly divisible by \(x^2+2x-3 \).

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Question 12 of 52

12. Question

1 point(s)

What must be added to polynomial \(f(x)=x^4+2x^3-2x^2+x-1 \) so that the resulting polynomial is exactly divisible by \(x^2+2x-3 \).

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Question 13 of 52

13. Question

1 point(s)

Find a quadratic polynomial whose zeroes are 2 and –6. Ve rify the relation between the coefficients and zeroes of the polynomial.

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Question 14 of 52

14. Question

1 point(s)

Find a quadratic polynomial whose zeroes are 2 and –6. Ve rify the relation between the coefficients and zeroes of the polynomial.

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Question 15 of 52

15. Question

1 point(s)

Can (x + 3) be the remainder on the division of a polynomial p(x) by (2x– 5)? Justify your answer.

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Question 16 of 52

16. Question

1 point(s)

Can (x + 3) be the remainder on the division of a polynomial p(x) by (2x– 5)? Justify your answer.

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Question 17 of 52

17. Question

1 point(s)

Find the zeroes of the polynomial \(2x^2-7x+3 \) and hence find the sum of product of its zeroes.

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Question 18 of 52

18. Question

1 point(s)

Find the zeroes of the polynomial \(2x^2-7x+3 \) and hence find the sum of product of its zeroes.

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Question 19 of 52

19. Question

1 point(s)

Check whether \(x^2+3x+1 \) is a factor of \(3x^4+5x^3-7x^2+2x+2 \).

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Question 20 of 52

20. Question

1 point(s)

Check whether \(x^2+3x+1 \) is a factor of \(3x^4+5x^3-7x^2+2x+2 \).

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Question 21 of 52

21. Question

1 point(s)

Find the zeroes of the quadratic polynomial \(x^2+7x+12 \) and verify the relationship between the zeroes and its coefïcients.

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Question 22 of 52

22. Question

1 point(s)

Find the zeroes of the quadratic polynomial \(x^2+7x+12 \) and verify the relationship between the zeroes and its coefïcients.

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Question 23 of 52

23. Question

1 point(s)

Divide \((2x^2+x-20) \) by \((x+3) \) and verify division algorithm.

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Question 24 of 52

24. Question

1 point(s)

Divide \((2x^2+x-20) \) by \((x+3) \) and verify division algorithm.

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Question 25 of 52

25. Question

1 point(s)

If \(\alpha \) and \(\beta \) are the zeroes of \(x^2+7x+12 \), then find the value of \(\dfrac{1}{\alpha}+\dfrac{1}{\beta}-2\alpha\beta \)

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Question 26 of 52

26. Question

1 point(s)

If \(\alpha \) and \(\beta \) are the zeroes of \(x^2+7x+12 \), then find the value of \(\dfrac{1}{\alpha}+\dfrac{1}{\beta}-2\alpha\beta \)

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Question 27 of 52

27. Question

1 point(s)

If \(\alpha \) and \(\beta \) are the zeroes of the polynomial \(2y^2+7y+5 \), write the value of \(\alpha+\beta+\alpha\beta \).

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Question 28 of 52

28. Question

1 point(s)

If \(\alpha \) and \(\beta \) are the zeroes of the polynomial \(2y^2+7y+5 \), write the value of \(\alpha+\beta+\alpha\beta \).

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Question 29 of 52

29. Question

1 point(s)

If the product of zeroes of the polynomial \(ax^2-6x-6 \) is \(4 \), find the value of \( a\).

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Question 30 of 52

30. Question

1 point(s)

If the product of zeroes of the polynomial \(ax^2-6x-6 \) is \(4 \), find the value of \( a\).

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Question 31 of 52

31. Question

1 point(s)

Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.

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Question 32 of 52

32. Question

1 point(s)

Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.

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Question 33 of 52

33. Question

1 point(s)

If one zero of the polynomial \((a^2+9)x^2+13x+6a \) is reciprocal of the other, find the value of \( a\).

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Question 34 of 52

34. Question

1 point(s)

If one zero of the polynomial \((a^2+9)x^2+13x+6a \) is reciprocal of the other, find the value of \( a\).

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Question 35 of 52

35. Question

1 point(s)

Find the zeroes of the quadratic polynomial \(f(x)=abx^2+(b^2-ac)x-bc \) and verify the relationship between the zeroes and its coefficients.

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Question 36 of 52

36. Question

1 point(s)

Find the zeroes of the quadratic polynomial \(f(x)=abx^2+(b^2-ac)x-bc \) and verify the relationship between the zeroes and its coefficients.

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Question 37 of 52

37. Question

1 point(s)

Find the zeroes of the quadratic polynomial \(p(x)=x^2-(\sqrt3+1)x+\sqrt3 \) and verify the relationship between the zeroes and its coefficients.

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Question 38 of 52

38. Question

1 point(s)

Find the zeroes of the quadratic polynomial \(p(x)=x^2-(\sqrt3+1)x+\sqrt3 \) and verify the relationship between the zeroes and its coefficients.

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Question 39 of 52

39. Question

1 point(s)

Find a cubic polynomial with the sum, sum of the products of its zeroes taken two at a time and product of its zeroes as 3, –1 and –3 respectively.

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Question 40 of 52

40. Question

1 point(s)

Find a cubic polynomial with the sum, sum of the products of its zeroes taken two at a time and product of its zeroes as 3, –1 and –3 respectively.

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Question 41 of 52

41. Question

1 point(s)

If \(\alpha \) and \(\beta \) are zeroes of the quadratic polynomial. \(f(x)=x^2-1 \), find a quadratic polynomial whose zeroes and \(\dfrac{2\alpha}{\beta} \) and \(\dfrac{2\beta}{\alpha} \)

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Question 42 of 52

42. Question

1 point(s)

If \(\alpha \) and \(\beta \) are zeroes of the quadratic polynomial. \(f(x)=x^2-1 \), find a quadratic polynomial whose zeroes and \(\dfrac{2\alpha}{\beta} \) and \(\dfrac{2\beta}{\alpha} \)

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Question 43 of 52

43. Question

1 point(s)

If the square of the difference of the zeroes of the quadratic polynomial \(f(x)=x^2+px+45 \) is equal to 144, find the value of \(p \).

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Question 44 of 52

44. Question

1 point(s)

If the square of the difference of the zeroes of the quadratic polynomial \(f(x)=x^2+px+45 \) is equal to 144, find the value of \(p \).

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Question 45 of 52

45. Question

1 point(s)

If the sum of the zeroes of the quadratic polynomial \(f(t)=kt^2+2t+3k \) is equal to their product, find the value of \(k \).

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Question 46 of 52

46. Question

1 point(s)

If the sum of the zeroes of the quadratic polynomial \(f(t)=kt^2+2t+3k \) is equal to their product, find the value of \(k \).

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Question 47 of 52

47. Question

1 point(s)

Find the zeroes of the quadratic polynomial \(x^2+\dfrac{7}{2}x+\dfrac{3}{4} \), and verify relationship between the zeroes and the coefficients.

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Question 48 of 52

48. Question

1 point(s)

Find the zeroes of the quadratic polynomial \(x^2+\dfrac{7}{2}x+\dfrac{3}{4} \), and verify relationship between the zeroes and the coefficients.

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Question 49 of 52

49. Question

1 point(s)

If \(\alpha \) and \(\beta \) are zeroes of the quadratic polynomial \(x^2-6x+a \); find the value of \(a \) if \(3\alpha+2\beta=20 \).

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Question 50 of 52

50. Question

1 point(s)

If \(\alpha \) and \(\beta \) are zeroes of the quadratic polynomial \(x^2-6x+a \); find the value of \(a \) if \(3\alpha+2\beta=20 \).

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Question 51 of 52

51. Question

1 point(s)

Divide \((6+19x+x^2-6x^2) \) by \((2+5x-3x^2) \) and verify the division algorithm

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Question 52 of 52

52. Question

1 point(s)

Divide \((6+19x+x^2-6x^2) \) by \((2+5x-3x^2) \) and verify the division algorithm

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Maths Class X Question Bank

Questions Bank-Essay Type-Polynomials – Class X

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