Answer:
x = [tex]\frac{1}{2}[/tex], x = 5
Step-by-step explanation:
Given
2x² - 11x + 5 = 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 = 2 × 5 = 10 and sum = - 11
The factors are - 1 and - 10
Use these factors to split the x- term
2x² - x - 10x + 5 = 0 ( factor the first/second and third/fourth terms )
x(2x - 1) - 5(2x - 1) = 0 ← factor out (2x - 1) from each term
(2x - 1)(x - 5) = 0
Equate each factor to zero and solve for x
2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]
x - 5 = 0 ⇒ x = 5
