Determine the zero(s) of the function y=6x^2+13x+5 show all of your steps.
To find the zero(s) of the function, we need to solve the equation y=6x^2+13x+5 for x when y equals zero.
Setting y=0, we have:
0 = 6x^2 + 13x + 5
This quadratic equation can be factored or solved using the quadratic formula. Let's use the quadratic formula to find the zeros.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 6, b = 13, and c = 5.
x = (-(13) ± √((13)^2 - 4(6)(5))) / (2(6))
Simplifying further:
x = (-13 ± √(169 - 120)) / 12
x = (-13 ± √49) / 12
x = (-13 ± 7) / 12
There are two possible solutions:
1) x = (-13 + 7) / 12 = -6/12 = -1/2
2) x = (-13 - 7) / 12 = -20/12 = -5/3
Therefore, the zeros of the function y=6x^2+13x+5 are x = -1/2 and x = -5/3.