Embibe Experts Solutions for Chapter: Polynomials, Exercise 1: Madhya Pradesh Board-2018

Algebraic expression $x^2+3\sqrt{x}-4$ is not a polynomial.

If $\alpha , \beta$ are the roots of quadratic equation $a{x}^2+bx+c=0$, then find the value of ${\alpha }^2+{\beta }^2$. 

Divide $2x^2+3x+1$ by $x+2$.

Any polynomial of degree $2$ can have at most two zeros.

Find the zeros of the polynomial $x^2-3$.

The graphs of $y=p\left(x\right)$ are given in figure below for some polynomials $p\left(x\right)$. Find the number of zeros of $p\left(x\right)$.

Find the zeros of the quadratic polynomial $x^2-2x-8$ and verify the relationship between the zeros and the coefficients.

Obtain all other zeroes of  $3x^4+6x^3-2x^2-10x-5$, if two of its zeroes are $\sqrt{\frac{5}{3}}$ and $-\sqrt{\frac{5}{3}}$.