Question

Find the values of k for which the quadratic equation 9 x square - 3k x + k is equal to zero has equal roots

Answer 1

Answer:

k = 0 and k = 4

Step-by-step explanation:

A quadratic a x² + b x + c has two equal roots if the discriminant Δ = b² - 4ac is equal to zero.

For the quadratic in the question, the discriminant is

Δ = ( -3k )² - ( 4 ) ( 9 ) ( k ) = 9 k² - 36 k = 9 k ( k - 4 )

This is equal to 0 when k = 0 and when k = 4.

So the given quadratic has two equal roots when k = 0 and when k = 4.