Question

Find the solution(s) to 2x2 – 5x – 3 = 0.

Answer 1

x = -
`(1)/(2)`, x = 3

Explanation:

Given

2x² - 5x - 3 = 0 ← in standard form

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

product = 2 × - 3 = - 6 and sum = - 5

The factors are - 6 and + 1

Use these factors to split the x- term

2x² - 6x + x - 3 = 0 ( factor the first/second and third/fourth terms )

2x(x - 3) + 1 (x - 3) = 0 ← factor out (x - 3) from each term

(x - 3)(2x + 1) = 0

Equate each factor to zero and solve for x

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = -
`(1)/(2)`

x - 3 = 0 ⇒ x = 3