Sarvesh K Verma Solutions for Chapter: Theory of Equations, Exercise 15: Introductory Exercise

Directions: Find the roots of the following equations.

$6{\mathrm{x}}^2+40=31\mathrm{x}$

Directions: Find the roots of the following equations.

$6 \left(\frac{\mathrm{y}-3}{2\mathrm{y}+1}\right)+1=5\sqrt{\frac{\mathrm{y}-3}{2\mathrm{y}+1}}, \mathrm{y}\ne \frac{1}{2}$

Directions: Find the roots of the following equations.

${\left(\mathrm{x}-\frac{1}{\mathrm{x}}\right)}^2+8\left(\mathrm{x}+\frac{1}{\mathrm{x}}\right)=29, \mathrm{x}\ne 0$

Directions: Find the roots of the following equations.

$\left(\frac{1}{\mathrm{x}+1}+\frac{1}{\mathrm{x}+5}\right)=\left(\frac{1}{\mathrm{x}+2}+\frac{1}{\mathrm{x}+4}\right):$

Discriminant of the equation $-3 x^{2}+2 x-8=0$ is :

If $-4$ is a root of the quadratic equation ${\mathrm{x}}^2-\mathrm{px}-4=0$ and the quadratic equation ${\mathrm{x}}^2-\mathrm{px}+\mathrm{k}=0$ has equal roots, find the value of $\mathrm{k}$ :

A two digit number is such that the product of its digits is $12.$ When $9$ is addded to the number, the digits interchange their places, find the number:

The sum of the squares to two natural consecutive odd numbers is $290$, then find the sum of the number.