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 will use the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

where \( a = 6 \), \( b = 13 \), and \( c = 5 \).

Step 1: Calculate the Discriminant

First, we need to calculate the discriminant \( b^2 - 4ac \):

\[ b^2 = (13)^2 = 169 \] \[ 4ac = 4 \times 6 \times 5 = 120 \] \[ b^2 - 4ac = 169 - 120 = 49 \]

Step 2: Apply the Quadratic Formula

Since the discriminant is positive (49), we will have two real and distinct zeros.

Now substituting \( a \), \( b \), and the discriminant into the quadratic formula:

\[ x = \frac{-13 \pm \sqrt{49}}{2 \times 6} \] \[ x = \frac{-13 \pm 7}{12} \]

Step 3: Calculate the Two Solutions

Now we have two cases based on the \( \pm \):

Case 1: \[ x = \frac{-13 + 7}{12} = \frac{-6}{12} = -\frac{1}{2} \]

Case 2: \[ x = \frac{-13 - 7}{12} = \frac{-20}{12} = -\frac{5}{3} \]

Final Result

Thus, the zeros of the quadratic function \( y = 6x^2 + 13x + 5 \) are:

\[ x = -\frac{1}{2} \quad \text{and} \quad x = -\frac{5}{3} \]

Answer 2

make it simpler and make it like a kid wrote it with at least 2-3 sentences

Answer 3

To find the zeros of the equation \( y = 6x^2 + 13x + 5 \), we can use a special formula called the quadratic formula. First, we figured out a number called the discriminant, which was 49. Then, we used the formula to find two answers: \( x = -\frac{1}{2} \) and \( x = -\frac{5}{3} \). So, the zeros of the function are -0.5 and -1.67!