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

Answer 1

To find the zeros of the quadratic function y = 6x^2 + 13x + 5, we need to solve the equation 6x^2 + 13x + 5 = 0.

To solve this equation, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 6, b = 13, and c = 5. Plugging these values into the quadratic formula, we get:

x = (-13 ± √(13^2 - 4(6)(5))) / (2(6))
x = (-13 ± √(169 - 120)) / 12
x = (-13 ± √49) / 12

Simplifying further, we have:

x = (-13 ± 7) / 12

This gives us two possible solutions:

x = (-13 + 7) / 12 = -6/12 = -1/2
x = (-13 - 7) / 12 = -20/12 = -5/3

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