Please help!

Question

FIND THE TYPE AND NUMBER OF SOLUTIONS FOR EACH EQUATION. 

a. x2(squared)-3x=-8 

b. x2(squared)+4x=-3

c. 2x2(squared)-12x=-18

Answer 1

For functions in the form f(x) = ax² + bx + c, the number and nature of roots is given the by determinant of the qualitative formula, b² - 4ac.

 

If the determinant > 0, two unequal real roots

If the determinant = 0, two identical real roots

If the determinant < 0, two unequal complex roots

 

A model so you can go the other two.

 

f(x) = x² - 3x + 8, a = 1, b = -3, c = 8

 

b² - 4ac

(-3)² - 4(1)(8)

9 - 32

-32, therefore there are two unequal complex roots.