Question

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

Answer 1

Hi Mate !!


Given equation :- 3x² - k√3x + 4 = 0

a = 3

b = ( - k√3 )

c = 4


• If the roots of the quadratic equation are equal then their discriminant is equal to Zero.

i.e, D = 0 ..... ( i )
and D = b² - 4ac ..... ( ii )


From ( i ) and ( ii )

b² - 4ac = 0

( - k√3 )² - 4 × 3 × 4 = 0

3k² - 48 = 0

3k² = 48

k² = 48/3

k² = 16

k = √16

k = ± 4


So, the value k will be satisfied by both +16 and -16 .

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