Determine the zero(s) of the quadratic function y=6x2+13x+5 . Show all steps.(
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.
To determine the zeros of the quadratic function y=6x^2+13x+5, we need to find the values of x where y is equal to zero.
Step 1: Set y=0.
0 = 6x^2+13x+5
Step 2: Factor the quadratic equation.
To factor the quadratic equation, we need to find two numbers whose product is (6 * 5) = 30, and whose sum is 13. The numbers that satisfy this condition are 10 and 3.
0 = (2x+1)(3x+5)
Step 3: Set each factor equal to zero and solve for x.
Setting 2x+1 = 0:
2x = -1
x = -1/2
Setting 3x+5 = 0:
3x = -5
x = -5/3
So, the zeros of the quadratic function y=6x^2+13x+5 are x = -1/2 and x = -5/3.
To determine the zeros of a quadratic function, we need to find the values of x for which y becomes zero.
The quadratic function given is y = 6x^2 + 13x + 5. To find the zeros, we set y equal to zero:
0 = 6x^2 + 13x + 5
Now, we can solve this quadratic equation using factoring, completing the square, or using the quadratic formula. In this case, factoring is the most efficient method.
Step 1: Factor the quadratic equation.
0 = (2x + 1)(3x + 5)
Step 2: Set each factor equal to zero and solve for x.
2x + 1 = 0 or 3x + 5 = 0
Step 3: Solve for x in both equations.
2x = -1 or 3x = -5
x = -1/2 or x = -5/3
Thus, the zeros of the quadratic function y = 6x^2 + 13x + 5 are x = -1/2 and x = -5/3.