Determining the roots

Question

Algebraically determine the exact roots of the equation: f(x)=4x²+16x+9

Answer 1

Begin by setting the equation equal to 0

4x² + 16x + 9 = 0

Using the quadratic formula with a =4, b = 16, and c = 9,

x = (-16 ± √(16² - 4*4*9))/(2*4)

x = (-16 ± √112)/8

x = (-16 ± 4√7)/8

x = (-4 ± √7)/2

Thus, one root is x = (-4 + √7)/2 and the other is x = (-4 - √7)/2.