Question

Find the solutions to the equation below. check all that apply

Answer 1

Answer:

A and E

Step-by-step explanation:

Given

20x² - 26x + 8 = 0 ( divide through by 2 )

10x² - 13x + 4 = 0

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 = 10 × 4 = 40 and sum = - 13

The factors are - 5 and - 8

Use these factors to split the x- term

10x² - 5x - 8x + 4 = 0 ( factor the first/second and third/fourth terms )

5x(2x - 1) - 4(2x - 1) = 0 ← factor out (2x - 1) from each term

(2x - 1)(5x - 4) = 0

Equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = $\frac{1}{2}$ → E

5x - 4 = 0 ⇒ 5x = 4 ⇒ x = $\frac{4}{5}$ → A