Question

If the quadratic equation $x^2-4x+k=0$ has equal roots , then find the value of k,

Answer 1

$x^2-4x+k=0$ is of the form $a{x}^2+bx+c=0$ where $a=1b=-4c=k$

Roots are equal$\Rightarrow$ Discriminant$=0$

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

$\Rightarrow {(-4)}^2-4\times 1\times k=0$

$\Rightarrow 16-4k=0$

$\Rightarrow -4k=-16$

$\therefore k=\frac{16}{4}=4$