Answer :
Answer:
1/4 and -1
Step-by-step explanation:
For a quadratic equation to have 2 equal root, the discriminant value must be equal to zero.
Discriminant D = b² - 4ac = 0
Given the equation
x^2 − 2(2k + 1)x + (k + 2) = 0
From the equation, a = 1, b = -2(2k+1), c = k+2
a = 1, b = -4k - 2, c = k+2
Substitute into the discriminant formula;
Recall that: b² - 4ac = 0
(-4k - 2)²-4(1)(k+2) = 0
16k²+16k + 4 - 4k - 8 =0
16k²+12k - 4 = 0
16k²+16k - 4k - 4 = 0
16k(k+1)-4(k+1) = 0
16k - 4 = 0 and k+1 = 0
16k = 4 and k = -1
k = 4/16 and k = -1
k = 1/4 and -1
Hence the required value of k is 1/4 and -1