Question

Find the value(s) of k if the quadratic equation below has equal roots 3x^2-k√3 x+4=0

Answer 1

a = 3
b = – k√3
c = 4



Discriminant = b² - 4ac
=> ( – k√3 )² - 4( 3 × 4 )

=> 3k² - 48


We know, for equal roots discriminant is 0



=> 3k² - 48 = 0
=> k² = ( 48 / 3 )
=> k² = 16
=> k = –4 or + 4
$.$

Answer 2

A quadratic equation has equal roots if

b^2 - 4ac = 0

Here, b = - k√3, a = 3, c = 4

Given equation is 3x^2 - k√3x + 4 = 0

Now, b^2 - 4ac = 0

(- k√3)^2 - 4(3)(4) = 0

3k^2 - 48 = 0

k^2 = 48 ÷ 3

k^2 = 16

k = ± 4