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What is/are the x-intercept, if any, of the function? f(x) = 10x^4 - 60x^2

Question:

What is/are the x-intercept, if any, of the function?

{eq}f(x) = 10x^4 - 60x^2 {/eq}

The intercepts of the function:

The intercepts of the function are the points where the graph touches the coordinate axes. These points, which are of the form (a, 0) and (0, b).

- To find the intercept of a function with the y-axis, we find f (0).

- To find the intercepts of a function with the x-axis, we make f (x) = 0 and solve for x.

Answer and Explanation:

Find the x-intercepts

{eq}\displaystyle f(x)=0 \,\,\, \rightarrow \,\,\, 10x^4 - 60x^2=0 \\ \displaystyle 10x^2(x^2-6)=0 \\ \displaystyle x=0 \,\, x=-\sqrt 6 \,\, \textrm {and} \,\, x=\sqrt 6 {/eq}

The x-intercepts of the function {eq}f(x) = 10x^4 - 60x^2 {/eq} are:

{eq}\Rightarrow \,\,\boxed{(0,0) }\\ \Rightarrow \,\,\boxed{(-\sqrt 6,0) }\\ \Rightarrow \,\,\boxed{(\sqrt 6,0) } {/eq}


Learn more about this topic:

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How to Find and Apply the Intercepts of a Line

from ELM: CSU Math Study Guide

Chapter 15 / Lesson 5
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