R. D. Sharma Solutions for Chapter: Quadratic Equations, Exercise 4: EXERCISE 4.4

Find the roots of the following quadratic equation (if they exist) by the method of completing the square.

$3x^2+11x+10=0$

If $\alpha$ and $\beta$ are roots then find the value of $3(\alpha -\beta )$ where, $(\alpha >\beta )$.

If $\alpha$ and $\beta$ are the two roots of the quadratic equation $2x^2+x-4=0$ and $\alpha -\beta =\frac{\sqrt{k}}{2}$, then find the value $k$.

Find the real roots of the following quadratic equations (if they exist) by the method of completing the square.

$2x^2+x+4=0$

In case of real roots does not exist, write No as answer.

Find the roots of the following quadratic equation (if they exist) by the method of completing the square.

$4x^2+4\sqrt{3}x+3=0$

If $\alpha$ and $\beta$ are the roots of the above quadratic equation than find the value of $\alpha -\beta$. 

Find the roots of the following quadratic equations (if they exist) by the method of completing the square.

$\sqrt{2}{x}^2-3x-2\sqrt{2}=0$

If $\alpha$ and $\beta$ are roots than find the value of $\sqrt{2}(\alpha -\beta )$, where $(\alpha >\beta )$

Find the roots of the following quadratic equations (if they exist) by the method of completing the square.

$\sqrt{3}{x}^2+10x+7\sqrt{3}=0$

If $\alpha$ and $\beta$ are roots of above equation, then find the value of $\sqrt{3}(\alpha -\beta )$, where $(\alpha >\beta )$.

Find the roots of the following quadratic equations (if they exist) by the method of completing the square.

$x^2-(\sqrt{2}+1)x+\sqrt{2}=0$.

If one root is $\sqrt{p}$ times other root then, find the value of $p$.

If the roots of the quadratic equation $x^2-4ax+4a^2-b^2=0$ are in the form of $ka\pm b$, then find the value of $k$.