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Solution of quadratic equations, Relation between roots and coefficients (only real roots to be considered). Practical problem on quadratic equations.

Find the values of k ε R subject to the following condition :
Two roots of $x^2 +(k - 2)x + (2k + 1) = 0$ are equal.

Option:
A. 12
B. - 1
C. 2
D. 0, 12
Answer: D . 0, 12

Justification:

Here, the roots of $x^2 + (k -2)x + 2k + 1 = 0$ being equal, Δ = 0.
.`. $(k - 2)^2 - 4(2k + 1) = 0$
.`. $k^2 - 4k + k - 8k - 4 = 0$
.`. $k^2 - 12k = 0$
.`. $k(k - 12) = 0$
.`. $k = 0$ or $k = 12.$

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