Find the value of k for which the quadratic equation (k-3)x2+6x+9=0 has two equal roots

Question

If the quadratic equation (k-3)x²+6x+9=0 has two equal roots then find the value of k

Answer 1

Given equation, (k-3)x²+6x+9=0

Here, a = k-3, b = 6, c = 9

Since roots are equal

So, b² - 4ac = 0

(6)² - 4.(k-3).9=0

36 + 36k+108 = 0

-36k +144= 0

-36k = - 144

k = 144/36

k = 4

The value of k so that the equation (k-3)x²+6x+9=0 has two equal roots is 4.