Answer:
see explanation
Step-by-step 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 = - [tex]\frac{3}{2}[/tex]
5x - 2 = 0 ⇒ 5x = 2 ⇒ x = [tex]\frac{2}{5}[/tex]
