Question

find the value of k if the quadratic equation 3 x square - K root 3 X + 4 is equals to zero has equal roots

Answer 1

let the roots be m and m
sum=2m=√3k/3...............(1)
product =m*m=4/3
m=2/√3.........(2)
put in (1)
2(2/√3)=√3k/3
k=4

Answer 2

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

It is in the form of ax^2 + bx + c = 0

Where $a =3, b = - k \sqrt{3}, c = 4$

Given that the equation has equal roots.

D = 0

b^2 - 4ac = 0

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

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

$3k^{2} = 48$

$k^{2} = \frac{48}{3}$

$k^{2} = 16$

k = 4 (or) -4.


Hope this helps!