Question

PLEASE HELP QUICK!!!!!!!!! Given the equation x2 + 4x + c = 0, determine a value for c that gives the equation: a) Two real solutions and find its solutions. b) Complex solution(s) and find its solution(s). c) Exactly one real solution and find its solution.

Answer 1

a. two (distinct) real solutions.

c = 3, x=¨{-1,-3}

b. two complex solutions

c = 17, x={-2+sqrt(13)i, -2-sqrt(13)i}

c. two coincident roots (i.e. one real solution)

c=4, x = {-2}, or x = {-2, -2}

Explanation:

Given:

x^2+4x+c =0

a. two (distinct) real solutions.

c = 3

(x+1)(x+3) = 0

x=¨{-1,-3}

b. two complex solutions

c = 17

x^2+4x+17=0

does not have real factors.

x={-2+sqrt(13)i, -2-sqrt(13)i}

c. two coincident roots (i.e. one real solution)

c=4

x^2+4x+4=0 => (x+2)^2 = 0 => perfect square

x = {-2}, or x = {-2, -2}