Question

Find a) alpha square+beta square and b) 1/alpha + 1/beta if p(x)=x²+8x+16

Answer 1

Given equation

$x^{2} +8x+16=0$

Solving, we get,

$\implies x^{2} +8x+16=0$

$\implies x^{2} +4x+4x+16=0$

$\implies x(x+4)+4(x+4)=0$

$\implies (x+4)(x+4)=0$

Now,

$x+4=0\\\implies x = -4$

Let α and β be -4

a) α² + β²

$= (-4)^{2} + (-4)^{2} \\= 16 + 16\\= \boxed{\boxed{\bold{32}}}}$

b) 1/α + 1/β

$= \dfrac{1}{-4} +\dfrac{1}{-4}$

$=\dfrac{2}{-4}$

$= \boxed{\boxed{\bold{\frac{-1}{2}}}}}}$