Embibe Experts Solutions for Chapter: Theory of Equation, Exercise 1: WBJEE 2020

If the equation $x^2-cx+d=0$ has roots equal to the fourth powers of the roots of $x^2+ax+b=0,$ where $a^2>4b,$ then the roots of $x^2-4bx+2b^2-c=0$ will be

The expression $a{x}^2+bx+c, (a,b$ and $c$ are real$)$ has the same sign as that of $a$ for all $x$ if

Let $z_1$ and $z_2$ be two imaginary roots of $z^2+pz+q=0,$ where $p$ and $q$ are real. The points $z_1,z_2$ and origin form an equilateral triangle if

If $P\left(x\right)=a{x}^2+bx+c$ and $Q\left(x\right)=-a{x}^2+dx+c$, where $ac\ne 0$ ($a,b,c,d$ are all real), then $P\left(x\right)·Q\left(x\right)=0$ has

Let $f$ and $g$ be differentiable on the interval $I$ and let $a, b\in I, a<b.$ Then

Let $f\left(x\right)=x^{13}+x^{11}+x^9+x^7+x^5+x^3+x+12$. Then

The equation $x^{{\left({\log }_{3}x\right)}^2-\frac{9}{2}{\log }_{3}x+5}=3\sqrt{3}$ has

Let $f\left(x\right)=x^4-4x^3+4x^2+c, c\in R.$ Then,