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AVprozaik [17]
2 years ago
9

If f(x)=x^3-12x^2+35x-24f(x)=x 3 −12x 2 +35x−24 and f(8)=0f(8)=0, then find all of the zeros of f(x)f(x) algebraically.

Mathematics
1 answer:
Neporo4naja [7]2 years ago
7 0

Answer:

The zeros of f(x) are: (x - 1), (x - 3) and (x - 8)

<em></em>

Step-by-step explanation:

Given

f(x)=x^3-12x^2+35x-24

f(8) = 0

Required

Find all zeros of the f(x)

If f(8) = 0 then:

x = 8

And x - 8 is a factor

Divide f(x) by x - 8

\frac{f(x)}{x - 8} = \frac{x^3-12x^2+35x-24}{x - 8}

Expand the numerator

\frac{f(x)}{x - 8} = \frac{x^3 - 4x^2 -8x^2 + 3x + 32x - 24}{x - 8}

Rewrite as:

\frac{f(x)}{x - 8} = \frac{x^3 - 4x^2 + 3x - 8x^2 +32x - 24}{x - 8}

Factorize

\frac{f(x)}{x - 8} = \frac{(x^2 - 4x + 3)(x - 8)}{x - 8}

Expand

\frac{f(x)}{x - 8} = \frac{(x^2 -x - 3x + 3)(x - 8)}{x - 8}

Factorize

\frac{f(x)}{x - 8} = \frac{(x - 1)(x - 3)(x - 8)}{x - 8}

\frac{f(x)}{x - 8} = (x - 1)(x - 3)

Multiply both sides by x - 8

f(x) = (x - 1)(x - 3)(x - 8)

<em>Hence, the zeros of f(x) are: (x - 1), (x - 3) and (x - 8)</em>

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Answer:

Correct option: c) infinitely many solutions

Step-by-step explanation:

We have an equation with two variables, so as we have a system with less equations (just one) than variables (two), we have an infinite number of solutions.

To find some solutions, we can choose values for x and then just calculate the value of y:

x = 0:

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ANSWER

y= - 4x + 18

EXPLANATION

The given line has equation;

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The slope of this line is

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The given line is parallel to this line so it has the same slope:

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The equation of this line is in the form:

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3 years ago
Find the x- and y-intercepts of the following equation:<br> 2x+3y=-24
Ilya [14]

Answer:

Algebra 

 Topics 

How do you find the intercepts of x2y−x2+4y=0?

Algebra  Graphs of Linear Equations and Functions  Intercepts by Substitution

2 Answers

Gió

Mar 24, 2015

For the intercepts you set alternately x=0 and y=0 in your function:

and graphically:

Answer link

Alan P.

Mar 24, 2015

On the X-axis y=0

So

x2y−x2+4y=0

becomes

x2(0)−x2+4(0)=0

→−x2=0

→x=0

On the Y-axis x=0

and the original equation

x2y−x2+4y=0

becomes

(0)2y−(0)2+4y=0

→y=0

The only intercept for the given equation occurs at (0,0)

Answer link

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