List of top Mathematics Questions on Polynomials asked in CBSE Class X

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

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

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

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 $.

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?

One zero of a quadratic polynomial is twice the other. If the sum of zeroes is (-6), find the polynomial.

If one zero of the polynomial $x^2 - 5x - c$ is (-1), find the value of c. Also, find the other zero.

An arch of a railway bridge, built on Chenab riverbed, is shown in the above diagram. It is a parabolic arch connecting two hills at P and Q. If the parabolic curve is represented by the polynomial p(x) = −0.0025x² − 0.025x + 136.
Observe the diagram and based on above information, answer the following questions: