Practice Questions – Polynomials – Class X

Polynomials of degree 1, 2 and 3 are called _______, _______ and _______respectively.

The zeroes of a polynomial p(x) are precisely the x-coordinates of the points where the graph of y = p(x) intersects the _____axis

A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most ______ zeroes.

If \( \alpha \ and \ \beta\) are the zeroes of the quadratic ploynomial \( ax^{2} + bx + c, then \ \alpha + \beta = \frac{-b}{\hspace{1cm}} \ and \ \alpha \beta = \frac{c}{\hspace{1cm}} \)

If \( \alpha, \beta, \gamma \) are the zeroes of cubic polynomial \(ax^{3} + bx^{2} + cx + d = 0, \ then \ \alpha+\beta+\gamma = \frac{-b}{\hspace{1cm}} \)

A quadratic polynomial in which the sum and product of whose zeroes are -3 and 2 is _______

_______is a cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time and product of its zeroes are 3, -8, -13.

If \( \alpha \ and \ \beta\) are zeroes of the polynomial \(2x^{2}-4x+5, \) then the values of \(\alpha^{2} + \beta^{2}\) is _______

The quadratic polynomial whose zeroes are \(\frac{3 + \sqrt{2}}{3 – \sqrt{2}}, \frac{3-\sqrt{2}}{3+\sqrt{2}} \) is _____

If \( \alpha \ and \ \beta\) are the zeroes of the polynomial \(x^{2}+8x+6\), then the polynomial formed when zeroes are \(1+\frac{\beta}{\alpha}, 1+\frac{\alpha}{\beta}\) is ______

If \(\alpha, \beta, \gamma\) are the zeroes of the polynomial \(f(x) = 2x^{3} + 6x^{2} – 4x + 9 \), then the value of \(\frac{1}{\alpha\beta} + \frac{1}{\beta\gamma} + \frac{1}{\gamma\alpha}\) is _______

If \(\alpha, \beta\) be the zeroes of the quadratic polynomial \(f(x) = x^{2} + px +45 \ and \ \left(\alpha – \beta\right)^{2} = 144\), then p is equal to _______

If \(\alpha, \beta\) be the zeroes of the polynomial \(f(x) = x^{2} – 5x – 1 \ then \ the \ value \ of \ \alpha^{2}\beta + \alpha\beta^{2}\) is ________

If the zeroes of the quadratic polynomial \(2x^{2}-8x-m \ are \ \frac{5}{2} \ and \ \frac{3}{2}\) respectively, then the value of m is __________

If \(\alpha, \beta\) are the zeroes of the polynomial \(f(x) = x^{2} – 12x + k \ such \ that \ \alpha – \beta = 2\), then the value of k is ________

If \(\alpha, \beta\) are the zeroes of the polynomial \(f(x) = x^{2} – 5x + k \ such \ that \ \alpha – \beta = 1\), then the value of k is ________

Sum of zeroes of \(2x^{2} – 8x + 6 \) is _________

A polynomial of degree 4 is known as __________ polynomial

If \( x = \frac{4}{3}\) is a zero of the polynomial \( f(x) = 6x^{3} – 11x^{2}+kx-20\) then the value of k is __________

If \(\alpha, \beta\) are the zeroes of the quadratic polynomial \(p(x) = 2x^{2} – 3x + 7 \ then \ \alpha^{3} + \beta^{3}\) is ________