Answer:
9
Step-by-step explanation:
If α and β are the zeros of ax² + bx + c = 0 , then
α + β = [tex]\frac{-b}{a}[/tex] ( sum of zeros ) and
αβ = [tex]\frac{c}{a}[/tex] ( product of zeros )
Given
x² + 5x + 8 = 0
with a = 1, b = 5, c = 8 , with zeros a and b, then
a + b = [tex]\frac{-5}{1}[/tex] = - 5
ab = [tex]\frac{8}{1}[/tex] = 8
Thus
(a + b)² = a² + 2ab + b² , that is
(- 5)² = a² + 2(8) + b²
25 = a² + 16 + b² ( subtract 16 from both sides )
9 = a² + b²