Question

If the equation $k{x}^2-5x+k=0$ has equal roots, find the value of ${}^{\prime }{k}^{\prime }$

Answer 1

$k{x}^2-5x+k=0$

Here $a=k,b=-5,c=k$

Given that the equation has equa roots.

Therefore,

$D=0$

$b^2-4ac=0$

$(-5)-4\left(k\right)\left(k\right)=0$

$25-4k^2=0$

$\Rightarrow 4k^2=25$

$\Rightarrow k=\pm \sqrt{\frac{25}{4}}=\pm \frac{5}{2}$

Hence the value of $k$ is $\pm \frac{5}{2}$.