Question

If alpha and beta are the roots of eq.
x^2-4x+ 16=0,
Find alpha^2 + beta^2
@MelissaHolmes @sarah786

Answer 1

the solutions are
2+(2*i)*sqrt(3), 2-(2*i)*sqrt(3)

Answer 2

do you know how you can get sum of roots and product of roots of a quadratic equation ?

Answer 3

for
\(ax^2+bx+c=0\)

sum of roots = \(\dfrac{-b}{a}\)

and product of roots = \(\dfrac{c}{a}\)

Answer 4

alpha^2 + beta^2 = -16

Answer 5

remember complex solutions come in conjugate pairs (a+bi) , ( a - bi)
and
(a+bi)^2 + ( a - bi)^2
= a^2+ 2abi - b^2 + a^2 - 2abi - b^2
= 2a^2 - 2b^2

Answer 6

when you have a+b and ab,
use this :
\(a^2+b^2 = (a+b)^2-2ab\)