Question

Find the value of $k$ if the quadratic equation $3x^2-k\sqrt{3}x+4=0$ equal roots.

Answer 1

Given:Roots are equal

$\Rightarrow$ Discriminant$=0$

$\Rightarrow b^2-4ac=0$ where $a=3,b=-k\sqrt{3},c=4$

$\Rightarrow {(-k\sqrt{3})}^2-4\times 3\times 4=0$

$\Rightarrow 3(k^2-16)=0$

$\Rightarrow k^2-16=0$

$\therefore k=4,-4$