Question

Find the roots of the equation 3x^2 − 17x + 10 = 0.

Answer 1

roots are x =
`(2)/(3)` , x = 5

Explanation:

given the quadratic equation

3x² - 17x + 10 = 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 = 3 × 10 = 30 and sum = - 17

The factors are - 15 and - 2

use these factors to split the x- term

3x² - 15x - 2x + 10 = 0 ( factor the first/second and third/fourth terms )

3x(x - 5) - 2(x - 5) = 0 ← factor out (x - 5) from each term

(x - 5)(3x - 2) = 0 ← in factored form

equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

3x - 2 = 0 ( add 2 to both sides )

3x = 2 ( divide both sides by 3 )

x =
`(2)/(3)`

the roots are x =
`(2)/(3)` , x = 5