Question

Find the roots. 3x2 - 5x+ 2 =0

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given

3x² - 5x + 2 = 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 = 3 × 2 = 6 and sum = - 5

The factors are - 3 and - 2

Use these factors to split the x- term

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

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

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

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

3x - 2 = 0 ⇒ 3x = 2 ⇒ x = $\frac{2}{3}$

Roots are x = 1, x = $\frac{2}{3}$