Question

Find the roots of the following equations, if they exist, by applying the quadratic formula:

3a²x² + 8abx + 4b² = 0

Answer 1

Given

3a²x² + 8abx + 4b² = 0

Comparing it with Ax² + Bx + C = 0.we get

A = 3a², B = 8ab and C = 4b²

Discriminant D is given by:

D = (B² - 4AC)

= (8ab)² - 4 x 3a² x 4b²

= 16a²b² > 0

Hence, the roots of the equation are real. 

Roots α and β are given by:

Thus, the roots of the equation are -2b/3a and -2b/a