A) Find the values of k for which the equation x 2 − 2(2k + 1)x + (k + 2) = 0 has 2 equal roots.

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

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step-by-step explanation: