Question

Each solution to x^2 + 5x + 8 = 0 can be written in the form x = a + b i, where a and b are real numbers. What is a + b^2?

Answer 1

Answer:

9/2

Step-by-step explanation:

solutions of x for given equation are:

$x_{1}$ = $\frac{-5+\sqrt{25-4(1)(8)} }{2(1)}$ = $\frac{-5 +\sqrt{7}i}{2}$  ----------(1)

now comparing (1) with a+bi

a = -5/2

b = $\sqrt{7}$

hence, a +b^2 = -5/2 + 7 = 9/2

Answer 2

Answer:

-3/4

Step-by-step explanation:

Sorry @9866012578 but your answer is wrong, we first find both of the roots, which from the quadratic formula gives us -5/2 -(i * sqrt(7)/2) and from the knowladge that when the root is not real the 2 solutions are A+Bi and A-Bi, since we know that A stays the same and B is getting squared and we also know anynumber that is real becomes positive we you square it so all the numbers of B will be negetive because we have to have i^2 which = -1 so we can choose either -5/2 -(i * sqrt(7)/2) to use or -5/2 +(i * sqrt(7)/2) and from both of them we get -3/4 as your answer.