Question

To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x – 30.

Factor out the GCF of .

Answer 1

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

Explanation:

Given

4x² + 2x - 30 = 0 ( divide through by 2 )

2x² + x - 15 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 15 = - 30 and sum = + 1

The factors are + 6 and - 5

Use these factors to split the x- term

2x² + 6x - 5x - 15 = 0 ( factor the first/second and third/fourth terms )

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

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

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

2x - 5 = 0 ⇒ 2x = 5 ⇒ x =
`(5)/(2)`

Answer 2

Question posted was incomplete. Here are the answers

What are the roots of the function y = 4x2 + 2x – 30?

To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x – 30.

Factor out the GCF of 2

Next, factor the trinomial completely. The equation becomes

0 = 2(2x – 5)(x + 3)

Use the zero product property and set each factor equal to zero and solve.

The roots of the function are –3 and 5/2

Explanation: