Question

Determine the zero(s) of the quadratic function y=6x^2+13x+5 . Show all steps.(2 points)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the zero(s) of the quadratic function, we need to set y equal to zero and solve for x.

So, we have 6x^2+13x+5 = 0.

Now we can use the quadratic formula to determine the values of x:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 6, b = 13, and c = 5.

Plugging in these values into the quadratic formula, we get:

x = (-(13) ± √((13)^2 - 4(6)(5))) / (2(6))

Simplifying further:

x = (-13 ± √(169 - 120)) / 12

x = (-13 ± √49) / 12

x = (-13 ± 7) / 12

So, the possible values of x are:

x1 = (-13 + 7) / 12

x1 = -6/12

x1 = -1/2

x2 = (-13 - 7) / 12

x2 = -20/12

x2 = -5/3

Therefore, the zero(s) of the quadratic function y=6x^2+13x+5 are x = -1/2 and x = -5/3.