Find the values of k ε R subject to the following condition :Two roots of $x^2 +(k - 2)

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.

A. 12

B. - 1

C. 2

D. 0, 12

E. None of the above

Answer: D. 0, 12

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 $k = 12.$

Posted in: Quadratic Equations - Algebra - Mathematics

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.

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.