Question

10x²+11x-6=0

`10 {x}^(2) + 11x - 6 = 0`
​

Answer 1

see explanation

Explanation:

Given

10x² + 11x - 6 = 0

To factorise the quadratic

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 × - 6 = - 60 and sum = + 11

The factors are + 15 and - 4

Use these factors to split the x- term

10x² + 15x - 4x - 6 = 0 ( factor the first/second and third/fourth terms )

5x(2x + 3) - 2(2x + 3) = 0 ← factor out (2x + 3) from both terms

(2x + 3)(5x - 2) = 0

Equate each factor to zero and solve for x

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = -
`(3)/(2)`

5x - 2 = 0 ⇒ 5x = 2 ⇒ x =
`(2)/(5)`