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QuestionFind the zeros of the function g(x)=5x2+14x+8g(x)=5x^{2}+14x+8 using the quadratic formula. What are the x-intercepts?

Studdy Solution

STEP 1

Assumptions1. The function is a quadratic function of the form ax+bx+cax^ + bx + c . The coefficients are a=5a =5, b=14b =14, and c=8c =8
3. We are looking for the zeros of the function, which are the same as the x-intercepts of the graph4. We will use the quadratic formula to find the zeros, which is given by x=−b±b−4acax = \frac{-b \pm \sqrt{b^ -4ac}}{a}

STEP 2

Let's plug the coefficients into the quadratic formula.x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}

STEP 3

Substitute a=5a =5, b=14b =14, and c=8c =8 into the formula.
x=−14±142−∗5∗82∗5x = \frac{-14 \pm \sqrt{14^2 -*5*8}}{2*5}

STEP 4

implify the expression under the square root.
x=−14±196−16010x = \frac{-14 \pm \sqrt{196 -160}}{10}

STEP 5

Calculate the value under the square root.
x=−14±3610x = \frac{-14 \pm \sqrt{36}}{10}

STEP 6

Take the square root of36.
x=−14±610x = \frac{-14 \pm6}{10}

STEP 7

Now, we have two possible solutions for x. Let's solve for each one.
First, let's solve for xx when we add the values under the square root.
x1=−14+610x1 = \frac{-14 +6}{10}

STEP 8

Calculate the value of x1x1.
x1=−810=−0.8x1 = \frac{-8}{10} = -0.8

STEP 9

Now, let's solve for xx when we subtract the values under the square root.
x2=−14−6x2 = \frac{-14 -6}{}

STEP 10

Calculate the value of x2x2.
x2=−2010=−2x2 = \frac{-20}{10} = -2The zeros of the function are x=−0.8x = -0.8 and x2=−2x2 = -2. These are also the x-intercepts of the graph of the function.
So, the correct choice is A. The zeros and the x-intercepts are the same. They are x=−0.8x = -0.8 and x2=−2x2 = -2.

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