Answer:
see explanation
Step-by-step explanation:
To find the x- intercepts, set y = 0, that is
2x² - 3x - 5 = 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
The factors are + 2 and - 5
Use these factors to split the x- term
2x² + 2x - 5x - 5 = 0 ( factor the first/second and third/fourth terms )
2x(x + 1) - 5(x + 1) = 0 ← factor out (x + 1) from each term
(x + 1)(2x - 5) = 0
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1 ⇒ (- 1, 0)
2x - 5 = 0 ⇒ 2x = 5 ⇒ x = [tex]\frac{5}{2}[/tex] ⇒ ([tex]\frac{5}{2}[/tex], 0)
