Concept Checkers – Polynomials – Class X

Which of the following is not a polynomial?

If \(p(y) = 3y^{4}-5y^{3}+y^{2}+8\), the p(-1) will be

Degree of Polynomial \( y^{3}-2y^{2}-\sqrt{3}y+\frac{1}{2}\)

The polynomials \(ax^{3}+3x^{2}-3 \ and \ 2x^{3}-5x+a \ when \ divided \ by \ x-4\) leaves the same reminder. The value of a is

The sum and the product of the zeroes of a quadratic polynomial are 2 and -15 respectively. The quadratic ploynomial is

If one zero of the quadratic polynomial \(2x^{2}-8x – m \ is \ \frac{5}{2} \)then the other zero is

If \(\alpha \ and \ \beta\) are the zeroes of the quadratic polynomial \(f(x) = x^{2}-x-4\), then the value of \(\frac{1}{\alpha} + \frac{1}{\beta} – \alpha\beta \) is

If \( \alpha, \beta \ and \ \gamma\) are the zeroes of the polynomial \(2x^{3}+x^{2}-13x+6\) then the value of \(\alpha \beta \gamma\) is

If \(\alpha, \beta, \gamma\) be the zeroes of the polynomial p(x) such that \(\alpha + \beta + \gamma = 3, \alpha \beta + \beta \gamma + \gamma \alpha = -10 \ and \ \alpha\beta\gamma = -24 \), then p(x) is

The value of k such that the quadratic polynomial \(x^{2}-(k+6)x+2(2k+1)\) has sum of the zeroes as half of their product is

If \(\alpha \ and \ \beta\) are the zeroes of the quadratic polynomial \(f(x) = x^{2}-4x+3\), then the value of \(\alpha^{4}\beta^{3} + \alpha^{3}\beta^{4}\) is

If the polynomial \(2x^{3}+ax^{2}+3x-5 \ and \ x^{3}+x^{2}-2x+a\) leave the same reminder when divided by x-2, then the value of a is

One of the factors of \((a^{2}-b^{2})(c^{2}-d^{2})-4abcd \) is

If one of zero of the polynomial \( f(x) = (k^{2} + 4)x^{2} + 13x + 4k \) is reciprocal of the other, then k is equal to

If \(\alpha \ and \ \beta \) are the zeroes of the polynomial \( f(x) = x^{2} -p(x+1) -d\) such that \((\alpha + 1)(\beta + 1) = 0\), then d is equal to

If the sum of the squares of zeroes of the quadratic polynomial \( f(x) = x^{2} – 8x – + k \) is 40, the value of k is

The graph of \( y = x^{3} – 4x \) cuts x-axis at (-2,0), (0,0) and (2,0). The zeroes of \(x^{3} – 4x \) are

The graph of the polynomial p(x) cuts the x-axis at 2 points and touch it at 4 points, The number of zeroes of p(x) is

If the sum of the zeroes of quadratic polynomial \(f(y) = ky^{2}+2y+3k\) is equal to their product, find the value of k

The zeroes of the quadratic polynomial \(100x^{2} + 50x + 99 \) are