Question

find the values of K if the quadratic equation 3 x square - K under root 3 X + 4 is equals to zero has equal roots
$3x {}^{2} - k \sqrt{3x} + 4 = 0$

Answer 1

D =root under bsquare - 4 AC =0
ksquare3 - 4 3 4
ksquare3 - 48
ksquare3 =48
ksquare =16
k =root under 16
k = 4
HENCE K = 4 answer

Answer 2

Given Quadratic Equation is 3x^2 - k$\sqrt{3x}$ + 4 = 0

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

Given that The Quadratic equation has real roots.

We know that if the roots are equal then the discriminant is 0.

b^2 - 4ac = 0

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

$3 k^{2} - 48 = 0$

$3 k^{2} = 48$

$k^{2} = 16$


k = 4 (or) k = -4.


Hope this helps!