Question

If $p$ is chosen at random in the interval $0\le p\le 5$,the probability that the equations $x^2+px+p/4+1/2=0$ are real is

• A. $1/5$
• B. $2/5$
• C. $4/5$
• D. $3/5$

Answer 1

Answer: (C)

$4/5$

For the roots of the equation to be real

$\Delta =\sqrt{b^2-4ac}$ should be greater than $0$

$\therefore p^2-4(\frac{p}{4}+\frac{1}{2})\ge 0$

$p^2-p-2\ge 0$

$(p-2)(p+1)\ge 0$

$\therefore p<-1$ or $p>2$ satisfies our condition.

$\therefore$ the probability of $0\le p\le 5$ giving real roots is $4/5$