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

How many real numbers $x$ satisfy the equation $3^{2x+2}-3^{x+3}-3^x+3=0?$

Evaluate $X$ in its simplest form then find sum of all digits of $X.$ Where $X$ is given as $X=\sqrt{2008+2007\sqrt{2008+2007\sqrt{2008+2007\sqrt{\dots .}}}}$

The ratio of roots of the equations $a{x}^2+bx+c=0$ and $p{x}^2+qx+r=0$ are equal. If $D_1$ and $D_2$ are respective discriminants, then what is $\frac{D_1}{D_2}$ equal to?

If $\cos \alpha$ and $\cos \beta (0<\alpha <\beta <\pi )$ are the roots of the quadratic equation $4x^2-3=0,$ then what is the value of $\sec \alpha \times \sec \beta ?$

If $x, y$ are positive real numbers satisfying the system of equations $x^2+y\sqrt{xy}=336, y^2+x\sqrt{xy}=112,$ then $x+y$ equals

In a class, the total numbers of boys and girls are in the ratio $4:3$. On one day it was found that $8$ boys and $14$ girls were absent from the class and that the number of boys was the square of the number of girls. What is the total number of students in the class?

The number of real solutions of $x-\frac{1}{x^2-4}=2-\frac{1}{x^2-4}$ is

If the roots of the equation $\frac{1}{x+p}+\frac{1}{x+q}=\frac{1}{r}$ are equal in magnitude and opposite is sign, then the product of roots is