Question

Use the discriminant to determine the number and type of solutions the equation has.

x2 + 6x + 12 = 0

two rational solutions

two irrational solutions

no real solution

one real solution

Answer 1

no real solutions

Explanation:

x² + 6x + 12 = 0

the general solution :

x = (-b ±sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 6

c = 12

the discriminate is (b² - 4ac).

so,

x = (-6 ± sqrt(6² - 4×1×12))/(2×1)

the discriminate is

6² - 4×12 = 36 - 48 = -12

this is negative, so via the square root of a negative number we get 2 complex (imaginary) solutions.