Answer:
x = 1 , x = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
2x² - 5x + 3 = 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 = 2 × 3 = 6 and sum = - 5
The factors are - 2 and - 3
Use these factors to split the x- term
2x² - 2x - 3x + 3 ( factor the first/second and third/fourth terms )
2x(x - 1) - 3(x - 1) = 0 ← factor out (x - 1) from each term
(x - 1)(2x - 3) = 0
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]
