R S Aggarwal and Veena Aggarwal Solutions for Exercise 2: Exercise 4B

Solve each of the following equations by using the method of completing the square:

${\mathrm{x}}^2-6\mathrm{x}+3=0$

If roots of the equation are $3\pm \sqrt{k}$, then find $k$.

Solve each of the following equations by using the method of completing the square:

${\mathrm{x}}^2+8\mathrm{x}-2=0$

If the roots of the equation are $(-4\pm 3\sqrt{k})$, then find $k$?

Solve each of the following equations by using the method of completing the square.

$3x^2-x-2=0$

Solve each of the following equations by using the method of completing the square.

$8x^2-14x-15=0$

Solve each of the following equations by using the method of completing the square.

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

Solve each of the following equations by using the method of completing the square.

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

Solve each of the following equations by using the method of completing the square.

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

By using the method of completing the square, show that the equation $2x^2+x+4=0$ has no real roots.