Question

A quadratic equation $ax^2 +bx +c =0$, with distinct coefficients is formed. If $a, b, c$ are chosen from the numbers 2, 3, 5, then the probability that the equation has real roots is

• A. $\frac{1}{3}$
• B. $\frac{2}{5}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$
• E. $\frac{2}{3}$

Answer 1

Answer: (A)

Total number of ways of assigning values 2,3 , 5 to $a, b, c,=3 !=6$
Now, for quadratic equation $a x^{2}+b x +c=0$ to have real roots $b^{2}-4 a c \geq 0 .$
This is possible only when $a=2, b=5, c=3$ or $a=3, b=5, c=2$
$\Rightarrow $ Required probability $-\frac{2}{6}-\frac{1}{3}$