Embibe Experts Solutions for Chapter: Polynomials, Exercise 1: Exercise

If the graph of a quadratic polynomial lies entirely above $x$-axis, then which one of the following is correct?

If $a-b$, $a$ and $a+b$ are zeroes of the polynomial $f\left(x\right)=2x^3-6x^2+5x-7$, write the value of $a$.

The shape of the graph of a quadratic polynomial $a{x}^2+bx+c \left(a\ne 0\right)$ is a _____.

If the graph of a quadratic equation $a{x}^2+bx+c=0$ lies entirely below the $x-\mathrm{axis}$, then the roots are _____ roots.

(real / non-real)

Factorize: $6{\left(3a-2b\right)}^2-15\left(3a-2b\right)-9$

The value of the polynomial $f\left(x\right)=4x^2-7$ at $x=2$ is _____.

For any quadratic polynomial $a{x}^2+bx+c \left(a\ne 0\right)$, the graph of corresponding equation $y=a{x}^2+bx+c$ is a parabola opening downwards if _____$<0$.

For any quadratic polynomial $a{x}^2+bx+c \left(a\ne 0\right)$, the graph of corresponding equation $y=a{x}^2+bx+c$ is a parabola opening _____ if, $a>0$. $\left(\mathrm{Upwards} / \mathrm{Downwards}\right)$