Determine the zero(s) of the quadratic function y=6x2+13x+5

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To find the zero(s) of the quadratic function y=6x^2+13x+5, we need to set y to 0 and solve for x.

0 = 6x^2 + 13x + 5

To simplify the equation, we can factor the quadratic or use the quadratic formula.

Using factoring, we need to find two numbers whose product is 5*6=30 and whose sum is 13. The numbers 10 and 3 satisfy these conditions.

0 = (2x + 1)(3x + 5)

Setting each factor equal to zero:

2x + 1 = 0
3x + 5 = 0

Solving for x:

2x = -1
x = -1/2

3x = -5
x = -5/3

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