List of top Mathematics Questions on Polynomials

The graph of \(y = f(x)\) is given. The number of zeroes of \(f(x)\) is :

2 is a zero of the polynomial function \[ f(x)=x^4+kx^3+22x^2-6x-20. \] If \(-2,\alpha,\beta\) are the roots of the equation \[ x^3+3x^2+2kx-40=0 \] and \(\alpha<\beta\), then \(2\alpha+3\beta=\)

If \(5\) is the remainder when \[ 2x^5+kx^4+5x^3-3x^2+2x-1 \] is divided by \[ x^2+x+1, \] then the quotient is:

If \( \alpha, \beta, \gamma \) are the roots of the equation \( x^3 - 3x + 1 = 0 \), then \( \frac{\alpha}{1-\alpha} + \frac{\beta}{1-\beta} + \frac{\gamma}{1-\gamma} = \)

If \( x^5 + ax^4 + bx^3 + cx^2 + 5x + d = 0 \) is an odd order reciprocal equation of second type and \( \frac{1+\sqrt{3}i}{2} \) is a root, then \( b-c = \)

The equation formed with the roots obtained by diminishing the roots of the equation \( x^{4}+3x^{3}-7x^{2}+4x+1=0 \) by 'h', does not contain the \( x^{2} \) term. If the possible values of such 'h' are \( h_{1}<0 \) and \( h_{2}>0, \) then which one of the following is true?

If \( x^{5}+ax^{4}+b death^{3}+cx^{2}+5x+e=0 \) is a reciprocal equation of second kind such that \( a+b=4 \) then the number of complex roots of this equation is

If $\alpha, \beta, \gamma$ are the zeroes of $4x^3 + 8x^2 - 6x - 2$, then the value of $\alpha\beta + \beta\gamma + \gamma\alpha$ is _____.

If \( \alpha \) and \( \beta \) are two zeroes of a polynomial \( f(x) = px^2 - 2x + 3p \) and \( \alpha + \beta = \alpha\beta \), then value of p is :

If \( \alpha, \beta \) are the zeroes of the quadratic polynomial \( px^2 + qx + r \), then find the value of \( \alpha^3\beta + \beta^3\alpha \).

\( f(x) \) is a 5 degree polynomial that has extremes at \( x = \pm 1 \) and \( \lim_{x \to 0} \frac{f(x)}{x^3} = 5 \), then \( f(2) - f(-2) \) is:

How many zeroes does p(x) = (x $-$ 2)(x + 3) have ?

The sum of zeroes of the quadratic polynomial $x^2 + 2x + 5$ will be :

Find the value of $k$ if $(x - 3)$ is a factor of the polynomial $x^3 - kx^2 + 15x - 6$.

A polynomial of degree three has:

Assertion (A) : The polynomial \(p(y) = y^{2 + 4y + 3}\) has two zeroes.
Reason (R) : A quadratic polynomial can have at most two zeroes.

Find the value of p, for which one zero of the quadratic polynomial \(px^2 - 14x + 8\) is 6 times the other.

Observe the graph of polynomial \(p(x)\). Number of zeroes of \(p(x)\) is

\(\alpha, \beta\) are zeroes of the polynomial \(p(x) = 3x^2 - 6x - 5\). Find the value of \(\frac{1}{\alpha^2} + \frac{1}{\beta^2}\).

If the zeroes of a polynomial \(p(x)\) are \(-3\) and \(8\), then \(p(x)\) equals

The graph of y = f(x) is given.
The number of zeroes of f(x) is :

Assertion (A) : The polynomial \(p(y) = y^2 + 4y + 3\) has two zeroes.
Reason (R) : A quadratic polynomial can have at most two zeroes.

If \(\alpha, \beta\) are the zeroes of the polynomial \(p(x) = x^2 - 3x - 1\), then find the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\).

Find a quadratic polynomial whose zeroes are \((5 - 2\sqrt{3})\) and \((5 + 2\sqrt{3})\).

Which of the following graphs represents a polynomial with both zeroes being positive?