Question

If a and b are the zeroes of the polynomial x2 + 5x + 8, then the value of a2 + b2

is..............(Pls help)​

Answer 1

9

Explanation:

If α and β are the zeros of ax² + bx + c = 0 , then

α + β =
`(-b)/(a)` ( sum of zeros ) and

αβ =
`(c)/(a)` ( product of zeros )

Given

x² + 5x + 8 = 0

with a = 1, b = 5, c = 8 , with zeros a and b, then

a + b =
`(-5)/(1)` = - 5

ab =
`(8)/(1)` = 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