Question

Determine the zero(s) of the quadratic function  y=6x^2+13x+5

. Show all steps.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the zero(s) of the quadratic function, we need to find the values of x for which y is equal to zero.

So, let's set y equal to zero and solve for x:

0 = 6x^2 + 13x + 5

This equation can be factored as:

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

To find the values of x, we set each factor equal to zero and solve for x:

2x + 1 = 0

2x = -1

x = -1/2

3x + 5 = 0

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.

Answer 2

[AI-generated answer — Explain Bot]

To determine the zeros of a quadratic function, we need to find the values of x for which y = 0. In other words, we need to solve the quadratic equation 6x^2 + 13x + 5 = 0.

We can solve this quadratic equation using the quadratic formula:
x = [-b ± √(b^2 - 4ac)] / 2a

In this equation, a, b, and c are the coefficients of the quadratic equation y = ax^2 + bx + c. In our case, a = 6, b = 13, and c = 5.

Let's substitute these values into the quadratic formula:
x = [-13 ± √(13^2 - 4(6)(5))] / (2(6))

Simplifying this expression further:
x = [-13 ± √(169 - 120)] / 12
x = [-13 ± √49] / 12
x = [-13 ± 7] / 12

So we have two possible values for x:
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.

Answer 3

[AI-generated answer — Step-by-Step Bot]

To determine the zero(s) of the quadratic function y = 6x^2 + 13x + 5, we need to find the values of x where y equals zero. In other words, we need to solve the equation 6x^2 + 13x + 5 = 0.

Step 1: Identify the coefficients a, b, and c in the quadratic equation.
In this case, a = 6, b = 13, and c = 5.

Step 2: Use the quadratic formula to solve the equation.
The quadratic formula is x = (-b ± √(b^2 - 4ac))/(2a).
Plugging in the values, we get x = (-13 ± √(13^2 - 4 * 6 * 5))/(2 * 6).

Step 3: Simplify the expression under the square root.
Calculating inside the square root, we get x = (-13 ± √(169 - 120))/(2 * 6).
Simplifying further, we have x = (-13 ± √49)/(12).

Step 4: Evaluate the square root.
The square root of 49 is 7, so we have x = (-13 ± 7)/(12).

Step 5: Find the two possible solutions.
We have two equations: x = (-13 + 7)/(12) and x = (-13 - 7)/(12).
Simplifying, we get x = -6/12 and x = -20/12.

Step 6: Simplify the solutions.
To simplify the fractions, we divide both the numerator and denominator by their greatest common divisor.
For x = -6/12, the greatest common divisor is 6. Dividing by 6, we get x = -1/2.
For x = -20/12, the greatest common divisor is 4. Dividing by 4, we get x = -5/3.

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