Question

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. $\frac{4}{9}$

Answer 1

Answer: (D)

$\frac{4}{9}$

$x^2+4x+c=0$

For roots to be real

$0\ge 0$

$16-4c\ge c$

$4\ge c$

$\therefore \{1,2,3,4\}$

$\therefore$ Probability $=\frac{4}{9}$