Determine the zero(s) of the quadratic function y=6x2+13x+5 . Show all steps. make it short
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
By factoring or using the quadratic formula, we can find the values of x that make the equation equal to zero.
Factoring:
0 = (2x + 1)(3x + 5)
Setting each factor equal to zero:
2x + 1 = 0 or 3x + 5 = 0
Solving for x:
2x = -1 or 3x = -5
x = -1/2 or x = -5/3
Therefore, the zeros of the quadratic function are x = -1/2 and x = -5/3.
To find the zeros of the quadratic function y = 6x^2 + 13x + 5, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 6, b = 13, and c = 5. Plugging in these values, we get:
x = (-(13) ± √((13)^2 - 4(6)(5))) / (2(6))
Simplifying further:
x = (-13 ± √(169 - 120)) / (12)
x = (-13 ± √49) / 12
x = (-13 ± 7) / 12
Therefore, the zeros of the quadratic function are:
x = (-13 + 7) / 12 = -1/2
x = (-13 - 7) / 12 = -5/2
So, the zeros of the function y = 6x^2 + 13x + 5 are -1/2 and -5/2.
To find the zeros of the quadratic function, follow these steps:
Step 1: Set the function equal to zero.
0 = 6x^2 + 13x + 5
Step 2: Factorize the quadratic equation, if possible. If not, use the quadratic formula.
In this case, the equation doesn't factorize easily, so we'll use the quadratic formula.
Step 3: Use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the given quadratic equation, a = 6, b = 13, and c = 5. Plugging these values into the quadratic formula, we have:
x = (-13 ± √(13^2 - 4*6*5)) / (2*6)
x = (-13 ± √(169 - 120)) / 12
x = (-13 ± √49) / 12
x = (-13 ± 7) / 12
Step 4: Simplify the expression.
We have two possibilities:
x1 = (-13 + 7) / 12 = -6 / 12 = -1/2
x2 = (-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.