A maths - Quadratic equation and inequalities

bonkysleuth SG

find the value of a and of b for which,

(a) x^2 + ax < b is only satisfied by -2 < x <4

(b) 2x^2 + a > bx is only satisfied by x < -2 or x>3

Answers (a) a= -2 , b= 8 (b) a=-12 , b = 2

please lend me a hand in solving this. having an exam tomorrow, so please do state the workings clearly. thanks!

eagle SG

me also have exam tmr, but well

a) x^2 + ax - b < 0
smiling curve smaller than 0, so roots at -2 and 4
so x^2 + ax - b = (x+2)(x-4) = x^2 -2x -8

hence a = -2,
-b = -8 => b=8

b) 2x^2 - bx + a > 0 or x^2 - b/2 x + a/2 > 0
smiling curve again, and roots at x=-2 and x=3
so x^2 - b/2 x + a/2 = (x+2)(x-3) = x^2 - 5x -6
a/2 = -6 => a = -12
-b/2 = -5 => b = 10