Determine the zero(s) of the quadratic function y=6x2+13x+5%0D%0A%0D%0A=%0D%0A6%0D%0A%0D%0A2%0D%0A+%0D%0A13%0D%0A%0D%0A+%0D%0A5%0D%0A . Show all steps.
To find the zeros of the quadratic function y = 6x^2 + 13x + 5, we need to set y equal to zero and solve for x.
0 = 6x^2 + 13x + 5
This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 6, b = 13, and c = 5.
To solve this equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values a = 6, b = 13, and c = 5, we get:
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
x1 = -6 / 12
x1 = -1/2
x2 = (-13 - 7) / 12
x2 = -20 / 12
x2 = -5/3
Therefore, the zeros of the quadratic function y = 6x^2 + 13x + 5 are x = -1/2 and x = -5/3.