Erickson Spencer
07/11/2023 · Primary School
Find the zeros, if any, of the quadratic function using the quadratic formula. What are the \( x \)-intercepts, if any, of the graph of the function? \( g(x)=5 x^{2}+9 x+4 \) Select the correct choice below and, if necessary, fill in the answer box to complete your cholce. (Simplity your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) A. The zeros and the x-intercepts are the same. They are \( \square \). The zeros and the xintercepts are different. The zeros are \( \square \), the x-intercepts are B. There is no real zero solution and no x-intercept.
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Solve the equation \( 5x^{2}+9x+4=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(5x^{2}+9x+4=0\)
- step1: Factor the expression:
\(\left(x+1\right)\left(5x+4\right)=0\)
- step2: Separate into possible cases:
\(\begin{align}&5x+4=0\\&x+1=0\end{align}\)
- step3: Solve the equation:
\(\begin{align}&x=-\frac{4}{5}\\&x=-1\end{align}\)
- step4: Rewrite:
\(x_{1}=-1,x_{2}=-\frac{4}{5}\)
The zeros of the quadratic function \(g(x) = 5x^{2} + 9x + 4\) are \(x = -1\) and \(x = -\frac{4}{5}\) or \(x = -0.8\).
Since the zeros of the function are the values of \(x\) where the function intersects the x-axis, the x-intercepts of the graph of the function are also \(x = -1\) and \(x = -\frac{4}{5}\) or \(x = -0.8\).
Therefore, the correct choice is:
A. The zeros and the x-intercepts are the same. They are \(x = -1\) and \(x = -\frac{4}{5}\) or \(x = -0.8\).
Quick Answer
A. The zeros and the x-intercepts are the same. They are \(x = -1\) and \(x = -\frac{4}{5}\).
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