Find the value of k for which the quadratic equation (k-12)x2+2(k-12)x+2=0 has two equal roots

Question

If the quadratic equation (k-12)x²+2(k-12)x+2=0 has two equal roots then find the value of k

Answer 1

Given equation, (k-12)x²+2(k-12)x+2=0

Where, a = k-12, 

b = 2(k-12), 

c = 2

Since roots are equal

So, b² - 4ac = 0

4(k-12)² - 4.(k-12).2=0

(k-12)² - (k-12)2= 0

(k-12) (k-12-2)= 0

(k-12) (k-14) = 0

(k-12) = 0, or  k-14 = 0

k = 12,               k = 14

The value of k so that the equation (k-12)x²+2(k-12)x+2=0 has two equal roots is 12 or 14.