A and b are roots of the equation 2x^2 +5x - 4. Calculate the value of (a - b)^2?

a + b = -5/2
ab = -4/2

1 Answer
Sep 6, 2017

14 1/4

Explanation:

Sum of roots, SoR = a + b = -5/2

Product of roots, PoR = a*b = -4/2 =-2

(a - b)^2 = a^2 + b^2 - 2ab->i

from
(a + b)^2 = a^2 + b^2 + 2ab, therefore
(a + b)^2 - 2ab = a^2 + b^2->a

plug in a into i
(a - b)^2 = (a + b)^2 - 2ab - 2ab
(a - b)^2 = (a + b)^2 - 4ab

Plug in values of SoR & PoR in above equation.
(a - b)^2 = (-5/2)^2 - 4(-2) = 25/4 + 8 = 14 1/4