Question

Find the nonzero value of k for which the roots of the quadratic equation `9x^2-3kx+k=0` are real and equal. 

Answer 1

The given equation is `9x^2-3kx+k=0` 

This is of the form `ax^2+bx+c=0,` where `a=9, b=-3k and c=k` 

∴ `D=b^2-4ac=(-3k)^2-4xx9xxk=9k^2-36k` 

The given equation will have real and equal roots if D = 0. 

∴` 9k^2-36k=0`  

⇒` 9k(k-4)=0` 

⇒ `k=0  or  k-4=0` 

⇒`k=0   or  k=4` 

But, k ≠ 0 (Given)
Hence, the required values of k is 4.