Question

If $b\in [-20,0],$ then the probability that the graph of $f\left(x\right)=16x^2+8(a+5)-7a-5$ is strictly lie above x-axis is given as below

• A. $\frac{1}{17}$
• B. $\frac{3}{20}$
• C. $\frac{13}{20}$
• D. None of these

Answer 1

The correct option is C $\frac{13}{20}$

To have $f(x$) always greater than $0,D<0$.
$64(a+5{)}^2+64(7a+5)<0(a{)}^2+17a+30<0(a+15)(a+2)<0a\in (-15,-2)$, length of interval $=13$
given a[20,0], length of interval $=20$
$P=13/20$