Question

find the value of k, if the quadratic equation 3x2-k
$\sqrt{}$
3x+4=0 has equal roots

Answer 1

A quadratic equation has equal roots if :-

b^2 - 4ac = 0

Here, b = $\bf\huge -k\sqrt{3}$ , a = 3, c = 4

Given equation is 3x^2 -  $\bf\huge -k\sqrt{3}x$  + 4 = 0

b^2 - 4ac = 0

$\bf\huge -k\sqrt{3}^2$ - 4(3)(4) = 0

3k^2 - 48 = 0

k^2 = 48 ÷ 3

k^2 = 16

k = 4