Polynomials — Class 10 Mathematics (Standard) PYQs

If sum and product of zeroes of a polynomial are $(-3)$ and $(-2)$ respectively, then a polynomial is

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 $p(x)=-0.0025x^2-0.025x+136$.
Observe the diagram and based on above information, answer the following questions :
(i) Write the co-ordinates of point A.
(ii) Find the span of the arch.
(iii) (a) Write the zeroes of the polynomial using diagram and verify the relationship between sum of zeroes and polynomials.
OR
(iii) (b) Find the values of $p(x)$ at $x = 100$ and $x = -100$. Are they same ?

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

If $\alpha$ and $\beta$ are the zeroes of polynomial $3x^2+6x+k$ such that $\alpha +\beta +\alpha \beta =-\frac{2}{3}$, then the value of $k$ is :

Two polynomials are shown in the graph below. The number of distinct zeroes of both the polynomials is :

Find the zeroes of the polynomial $p(x)=x^2+\frac{4}{3}x-\frac{4}{3}$.

If the zeroes of the polynomial $x^2+ax+b$ are in the ratio $3:4$, then prove that $12a^2=49b$.

The sum of the zeroes of the polynomial $p(x)=5x-7x^2+3$ is :

If $-4$ is a zero of the polynomial $p(x)=x^2-x-(2+2k)$, then the value of $k$ is :

If $p$ and $q$ are zeroes of the polynomial $p(y)=21y^2-y-2$, then find the value of $(1 - p)(1 - q)$.