Question

Solve the quadratic equation using any algebraic method. Show all work that leads to your answer.

6x² + 23x + 20 = 0

Answer 1

x = -
`(5)/(2)` , x = -
`(4)/(3)`

Explanation:

6x² + 23x + 20 = 0 ( factorise the left side )

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

product = 6 × 20 = 120 and sum = 23

the factors are + 8 and + 15

use these factors to split the x- term

6x² + 8x + 15x + 20 = 0 ( factor the first/second and third/fourth terms )

2x(3x + 4) + 5(3x + 4) = 0 ← factor out (3x + 4) from each term

(3x + 4)(2x + 5) = 0

equate each factor to zero and solve for x

2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = -
`(5)/(2)`

3x + 4 = 0 ⇒ 3x = - 4 ⇒ x = -
`(4)/(3)`