Question

The quadratic equation which has D = 0 and a root as $\frac{1}{10}$ is

• A. $x^2-20x-100=0$
• B. $x^2-100x-100=0$
• C. $100x^2-20x+1=0$
• D. $100x^2-20x+100=0$

Answer 1

The correct option is C $100x^2-20x+1=0$

Since D = 0, the quadratic equation has roots which are real and equal.

The roots of the equation are $\frac{1}{10}$, $\frac{1}{10}$

Sum of the roots $=\frac{1}{10}+\frac{1}{10}=\frac{1}{5}$ ,

Product of the roots $=\frac{1}{10}\times \frac{1}{10}=\frac{1}{100}$

So the required quadratic equation is:

$\Rightarrow x^2-\frac{1}{5}x+\frac{1}{100}=0$

$\Rightarrow 100x^2-20x+1=0$