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QuestionFind the zeros of the function g(x)=4x2+9x+5g(x)=4 x^{2}+9 x+5 using the quadratic formula. What are the x-intercepts?

Studdy Solution

STEP 1

Assumptions1. The quadratic function is g(x)=4x+9x+5g(x)=4x^{}+9x+5 . We are to find the zeros of this function using the quadratic formula3. The quadratic formula is x=−b±b−4acax=\frac{-b\pm\sqrt{b^{}-4ac}}{a} where aa, bb, and cc are coefficients of the quadratic equation ax+bx+c=0ax^{}+bx+c=0

STEP 2

First, we identify the coefficients aa, bb, and cc from the given quadratic function.
a=4,b=9,c=5a =4, b =9, c =5

STEP 3

Now, we plug these values into the quadratic formula.
x=−b±b2−ac2ax=\frac{-b\pm\sqrt{b^{2}-ac}}{2a}x=−9±92−∗∗52∗x=\frac{-9\pm\sqrt{9^{2}-**5}}{2*}

STEP 4

implify the expression inside the square root.
x=−9±81−808x=\frac{-9\pm\sqrt{81-80}}{8}

STEP 5

Calculate the value inside the square root.
x=−9±18x=\frac{-9\pm\sqrt{1}}{8}

STEP 6

implify the square root.
x=−9±18x=\frac{-9\pm1}{8}

STEP 7

Now, we have two solutions, one for the plus sign and one for the minus sign.
x1=−9+1,x2=−9−1x_{1}=\frac{-9+1}{}, x_{2}=\frac{-9-1}{}

STEP 8

Calculate the two solutions.
x1=−88=−1,x2=−108=−1.25x_{1}=\frac{-8}{8}=-1, x_{2}=\frac{-10}{8}=-1.25The zeros and the x-intercepts are the same. They are x1=−1x_{1}=-1 and x2=−1.25x_{2}=-1.25.

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