List of top Mathematics Questions on Polynomials

If one of the zeroes of the quadratic polynomial \((\alpha - 1)x^2 + \alpha x + 1\) is \(-3\), then the value of \(\alpha\) is:

If one of the zeroes of the quadratic polynomial \((\alpha - 1)x^2 + \alpha x + 1\) is \(-3\), then the value of \(\alpha\) is:

Assertion (A): Zeroes of a polynomial \(p(x) = x^2 − 2x − 3\) are -1 and 3.
Reason (R): The graph of polynomial \(p(x) = x^2 − 2x − 3\) intersects the x-axis at (-1, 0) and (3, 0).

The graph of a polynomial intersects the y-axis at one point and the x-axis at two points. The number of zeroes of this polynomial are :

Assertion (A): Zeroes of a polynomial \(p(x) = x^2 − 2x − 3\) are -1 and 3.
Reason (R): The graph of polynomial \(p(x) = x^2 − 2x − 3\) intersects the x-axis at (-1, 0) and (3, 0).

The graph of a polynomial intersects the y-axis at one point and the x-axis at two points. The number of zeroes of this polynomial are :

The HCF of two polynomials \( p(x) = 4x^2 (x^2 - 3x + 2) \) and \( q(x) = 12x(x - 2)(x^2 - 4) \) is \( 4x(x - 2) \). The LCM of these polynomials is:

Find the zeroes of the polynomial $f(t) = t^2 + 4\sqrt{3}t - 15$ and verify the relationship between the zeroes and the coefficients of the polynomial.

Find the zeroes of the polynomial $f(t) = t^2 + 4\sqrt{3}t - 15$ and verify the relationship between the zeroes and the coefficients of the polynomial.

For what value of \(k\), the product of zeroes of the polynomial \(kx^2 - 4x - 7\) is 2?

Let \( f(x) \) be a polynomial function satisfying \[ f(x) \cdot f\left(\frac{1}{x}\right) = f(x) + f\left(\frac{1}{x}\right). \] If \( f(4) = 65 \) and \( I_1, I_2, I_3 \) are in GP, then \( f'(I_1), f'(I_2), f'(I_3) \) are in:

Consider \(p(x)\) a polynomial of degree 5 having extremum at \(x=-1,1\). Given \[ \lim_{x\to0}\left(\frac{p(x)}{x}-2\right)=4, \] the value of \(p[1]\) (greatest integer function) is}

If \[ \Delta= \begin{vmatrix} f(x) & f\!\left(\dfrac{1}{x}\right)+f(x)\\ 1 & f\!\left(\dfrac{1}{x}\right) \end{vmatrix} =0 \] where \(f(x)\) is a polynomial and \(f(2)=17\), then \(f(5)=\) ?

The sum of zeroes of the polynomial \(3x^2 + 5x + 2\) will be

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

Find the zeroes of the quadratic polynomial $x^2 + 7x + 10$ and verify the relationship between the zeroes and the coefficients.

Maximum number of zeroes of a cubic polynomial will be:

If \( p(y) = (y+1)(y^3+2)(y^4+6) \) and \( g(y) = y^2 - 3y +1 \), then the degree of \( \frac{p(y)}{g(y)} \) is: