Find the value of k for which the quadratic equation x2-(k+4)x+2k+5=0 has two equal roots

Question

If the quadratic equation x²-(k+4)x+2k+5=0 has two equal roots then find the value of k

Answer 1

Given equation, x²-(k+4)x+2k+5=0

Here, a = 1, b = -(k+4), c = 2k+5

Since roots are equal

So, b² - 4ac = 0

{-(k+4)}² - 4.1.(2k+5)=0

k²+8k+16-8k-20 =0

k² - 4 = 0

k² = 4

k² = 2²

k= ± 2

The value of k so that the equation x²-(k+4)x+2k+5=0 has equal roots is 2 or -2.