Q. The probability of choosing randomly a number $c\$from the set {1, 2, 3,…..,9} such that the quadratic equation $x^{2} + 4x + c = 0$ has real roots is
A) $\frac{1}{9}$
B) $\frac{2}{9}$
C) $\frac{3}{9}$
D) $\frac{4}{9}$
Explanation
(d)
Given, $x^{2} + 4x + c = 0$
For real roots, $D = b^{2} - 4ac \geq 0$
$= 16 - 4c \geq 0$
$\Rightarrow c = 1,\ 2,\ 3,\ 4$ will satisfy the above inequality
$\therefore Required\ probability = \frac{4}{9}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.