Determine the zero(s) of the function y=6x^2+13x+5 . Show all of your steps. Hint: You can use factoring or the quadratic formula. (2 points)
To find the zeros of the function, we need to set y equal to zero and solve for x.
0 = 6x^2 + 13x + 5
Next, we can try factoring the equation. However, in this case, the equation does not easily factor. Therefore, we will use the quadratic formula.
The quadratic formula is given as:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 6, b = 13, and c = 5.
x = (-13 ± √(13^2 - 4(6)(5))) / (2(6))
x = (-13 ± √(169 - 120)) / 12
x = (-13 ± √49) / 12
x = (-13 ± 7) / 12
This gives us two possible solutions:
x1 = (-13 + 7) / 12 = -6/12 = -1/2
x2 = (-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.