# 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

Sep 6, 2017

$14 \frac{1}{4}$

#### Explanation:

Sum of roots, SoR $= a + b = - \frac{5}{2}$

Product of roots, PoR $= a \cdot b = - \frac{4}{2} = - 2$

${\left(a - b\right)}^{2} = {a}^{2} + {b}^{2} - 2 a b$$\to i$

from
${\left(a + b\right)}^{2} = {a}^{2} + {b}^{2} + 2 a b$, therefore
${\left(a + b\right)}^{2} - 2 a b = {a}^{2} + {b}^{2}$$\to a$

plug in $a$ into $i$
${\left(a - b\right)}^{2} = {\left(a + b\right)}^{2} - 2 a b - 2 a b$
${\left(a - b\right)}^{2} = {\left(a + b\right)}^{2} - 4 a b$

Plug in values of SoR & PoR in above equation.
${\left(a - b\right)}^{2} = {\left(- \frac{5}{2}\right)}^{2} - 4 \left(- 2\right) = \frac{25}{4} + 8 = 14 \frac{1}{4}$