Question

If roots of quadratic equation 2x² - kx +k = 0 are real and equal, then find k.

Answer 1

Given quadratic equation is= 2x² - kx +k = 0
On comparing with standard form of quadratic equation i.e ax² + bx + c =0,

Here, a = 2 , b= -k, c= k

D(discriminant)= b²-4ac
= (-k)² - 4× 2× k
= k² -8k
= k (k -8)

Since, roots of given equation are real and equal. D= 0

0 =  k (k -8)
k = 0 or k-8= 0
k = 0 or k = 8

Hence, required value of k is 0 & 8.

HOPE THIS WILL HELP YOU...

Answer 2

As roots are real and equal then the 
Discriminant ⇒  b²-4ac    = 0
                  (-k)²-4(2)(k)    = 0
                           k² - 8k   = 0
              k² - 8k + 0k + 0  = 0
              k(k-8) + 0(k-8)   = 0
                       (k+0)(k-8) = 0

Then k = 8 , 0

:)Hope This Helps!!!