Question

Find the value of a and of b for which
(a) the solution of x2 + ax < b is
-2<x < 4​

Answer 1

Answer: $a = -2$

$b = 8$

Step-by-step explanation:

Given :

$x^{2} +ax<b$

re - writing the equation , we have

$x^{2} +ax-b<0$

we need to find the value of a and b for which -2<x < 4 , this means that the roots of the quadratic equation are -2<x < 4.

The formula for finding the quadratic equation when the roots are known is :

$x^{2}$ - sum of roots(x) + product of root = 0

sum of roots = -2 + 4 = 2

product of roots = -2 x 4 = -8

substituting into the formula , we have:

$x^{2} -2x-8=0$ , which could be written in inequality form as

$x^{2} -2x-8<0$

comparing with $x^{2} +ax-b<0$ , it means that :

$a = -2$

$b = 8$