Question

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

Answer 1

`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`