Find the zeros of the function algebraically. f(x) = 4xª – 25x² Step 1 To find the zeros, set the function equal to zero. 0 - 4x4 – 25x2 Step 2 Factor out the monomial expression. 0 - x*(4 -25 Step 3 Set each factor equal to zero to solve for x. First, set the monomial factor equal to zero and solve. (Enter your answers as a comma-separated list.) - 0 = x - 0 Next, set the binomial factor equal to zero and solve. (4x2 - 25) = 0 = 25 = 5 _ 5 (Enter vour answers as a comma-separated list.)
Find the zeros of the function algebraically. f(x) = 4xª – 25x² Step 1 To find the zeros, set the function equal to zero. 0 - 4x4 – 25x2 Step 2 Factor out the monomial expression. 0 - x*(4 -25 Step 3 Set each factor equal to zero to solve for x. First, set the monomial factor equal to zero and solve. (Enter your answers as a comma-separated list.) - 0 = x - 0 Next, set the binomial factor equal to zero and solve. (4x2 - 25) = 0 = 25 = 5 _ 5 (Enter vour answers as a comma-separated list.)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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![**Finding the Zeros of the Function Algebraically**
Given function:
\[ f(x) = 4x^4 - 25x^2 \]
**Step 1**
To find the zeros, set the function equal to zero.
\[ 0 = 4x^4 - 25x^2 \]
**Step 2**
Factor out the monomial expression.
\[ 0 = x^2 (4x^2 - 25) \]
**Step 3**
Set each factor equal to zero to solve for \( x \).
First, set the monomial factor equal to zero and solve:
\[ x^2 = 0 \implies x = 0 \]
Next, set the binomial factor equal to zero and solve.
\[ 4x^2 - 25 = 0 \]
\[ 4x^2 = 25 \]
\[ x^2 = \frac{25}{4} \]
\[ x = \pm \frac{5}{2} \]
So, the solutions are:
\[ x = 0, \frac{5}{2}, -\frac{5}{2} \]
(Enter your answers as a comma-separated list.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11ff91fa-fde1-47cc-bcac-170d9b2fe11c%2Fb17a77cc-878f-45b8-8964-0e1b6c4eed25%2Fpwzv3zo_processed.png&w=3840&q=75)
Transcribed Image Text:**Finding the Zeros of the Function Algebraically**
Given function:
\[ f(x) = 4x^4 - 25x^2 \]
**Step 1**
To find the zeros, set the function equal to zero.
\[ 0 = 4x^4 - 25x^2 \]
**Step 2**
Factor out the monomial expression.
\[ 0 = x^2 (4x^2 - 25) \]
**Step 3**
Set each factor equal to zero to solve for \( x \).
First, set the monomial factor equal to zero and solve:
\[ x^2 = 0 \implies x = 0 \]
Next, set the binomial factor equal to zero and solve.
\[ 4x^2 - 25 = 0 \]
\[ 4x^2 = 25 \]
\[ x^2 = \frac{25}{4} \]
\[ x = \pm \frac{5}{2} \]
So, the solutions are:
\[ x = 0, \frac{5}{2}, -\frac{5}{2} \]
(Enter your answers as a comma-separated list.)
Transcribed Image Text:Therefore, the zeros of the function are the following. (Enter your answers as a comma-separated list.)
x = 0, \(\frac{5}{2}\), \(-\frac{5}{2}\)
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