# The Complete Set of Values of K, for Which the Quadratic Equation X 2 − K X + K + 2 = 0 Has Equal Roots, Consists of - Mathematics

MCQ

The complete set of values of k, for which the quadratic equation  $x^2 - kx + k + 2 = 0$ has equal roots, consists of

#### Options

• $2 + \sqrt{12}$

• $2 \pm \sqrt{12}$

• $2 - \sqrt{12}$

• $- 2 - \sqrt{12}$

#### Solution

$2 \pm \sqrt{12}$

$\text { Since the equation has real roots } .$

$\Rightarrow D = 0$

$\Rightarrow b^2 - 4ac = 0$

$\Rightarrow k^2 - 4\left( 1 \right)\left( k + 2 \right) = 0$

$\Rightarrow k^2 - 4k - 8 = 0$

$\Rightarrow k = \frac{4 \pm \sqrt{16 - 4\left( 1 \right)\left( - 8 \right)}}{2\left( 1 \right)}$

$\Rightarrow k = \frac{4 \pm 2\sqrt{12}}{2}$

$\Rightarrow k = 2 \pm \sqrt{12}$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 14 Quadratic Equations
Q 1 | Page 16