Question

Solve the equation below using factorising. 10y² – 11y − 6 = 0 - Give each answer as an integer or as a fraction in its simplest form.​

Answer 1

y = -
`(2)/(5)` , y =
`(3)/(2)`

Explanation:

10y² - 11y - 6 = 0

consider the factors of the product of the y² term and the constant term which sum to give the coefficient of the y - term

product = 10 × - 6 = - 60 and sum = - 11

the factors are - 15 and + 4

use these factors to split the y- term

10y² - 15y + 4y - 6 = 0 ( factor the first/second and third/fourth terms )

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

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

equate each factor to zero and solve for y

5y + 2 = 0 ⇒ 5y = - 2 ⇒ y = -
`(2)/(5)`

2y - 3 = 0 ⇒ 2y = 3 ⇒ y =
`(3)/(2)`