Question

Solve 5x2 + 13x + 6 = 0

Answer 1

Answer:

x = - 2, x = - $\frac{3}{5}$

Step-by-step explanation:

Given

5x² + 13x + 6 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 5 × 6 = 30 and sum = + 13

The factors are + 10 and + 3

Use these factors to split the x- term

5x² + 10x + 3x + 6 = 0 ( factor the first/second and third/fourth terms )

5x(x + 2) + 3(x + 2) = 0 ← factor out (x + 2) from each term

(x + 2)(5x + 3) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

5x + 3 = 0 ⇒ 5x = - 3 ⇒ x = - $\frac{3}{5}$