Question

The values of k for which the roots are real and equal of the following equation $k{x}^2-2\sqrt{5}x+4=0$ is $k=\frac{5}{4}$

• A. True
• B. False

Answer 1

The correct option is A True

$\Rightarrow$ Given quadratic equation is $k{x}^2-2\sqrt{5}x+4=0$, comparing it with $a{x}^2+bx+c=0$.

$\Rightarrow$ We get, $a=k,b=-2\sqrt{5}$ and $c=4$

$\Rightarrow$ It is given that roots are real and equal.

$\therefore$ $b^2-4ac=0$

$\Rightarrow$ $(-2\sqrt{5}{)}^2-4(k\left)\right(4)=0$

$\Rightarrow$ $20-16k=0$

$\Rightarrow$ $16k=20$

$\Rightarrow$ $k=\frac{20}{16}$

$\Rightarrow$ $k=\frac{5}{4}$

$\therefore$ Given value of $k$ is correct.