Question

Determine the zero(s) of the function y=6x^2+13x+5

. Show all of your steps.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the zeros of the function, we need to find the values of x for which y=0.

To factor the quadratic, we need to find two numbers that multiply to give the constant term (5) and add up to give the coefficient of the middle term (13). In this case, those numbers are 1 and 5:

y = 6x^2 + 13x + 5

= 6x^2 + 1x + 5x + 5

= (6x^2 + 1x) + (5x + 5)

= x(6x + 1) + 5(6x + 1)

= (x + 5)(6x + 1)

Now, we can set each factor equal to zero:

x + 5 = 0

x = -5

and

6x + 1 = 0

6x = -1

x = -1/6

Therefore, the zeros of the function are x = -5 and x = -1/6.