Question

Can anyone explain to me how to get the answer? (Answer is provided, 40 points)

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

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

Factor out the GCF: The GCF is 2.

Next, factor the trinomial completely. According to the answer chart, the answer to this is 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: According to the answer chart, the roots are -3 and 5/2.

Actual Question from me: If anyone can explain to me how 0 = 2(2x - 5)(x + 3) is achieved, I'd greatly appreciate it.

Answer 1

Here, root means points/point on the x-axis where the equation touches or passes through.

Examples would be (1, 0), (4, 0), (12, 0).

From the example you can notice that all of these points have value of y = 0.

That's why you put y = 0 in the equation to find points on the x-axis.

y = 4x^2 + 2x – 30

0 = 4x^2 + 2x – 30

0 = 2( 2x^2 + x - 15 ) (Factor out GCF 2)

This equation is in the form of ax^2+bx+c

Here,

a × c is 2 × -15 = -30 and b = 1

We want two numbers that multiply together to make -30, and add up to 1

So, 6 and -5 is right answer (6× -5 = -30, and 6 - 5 = 1)

Now,

0 = 2( 2x^2 + 6x - 5x - 15 )

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

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