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Chapter 4: Q. 67 (page 210)

In Problems 63鈥�72, find the real solutions of each equation.

3x3-x2-15x+5=0

Short Answer

Expert verified

The real solution of the equation are13,5,-5.

Step by step solution

01

Step 1. Finding the possible number of zeros 

The given equation is 3x3-x2-15x+5=0

The given function is of degree three, so it has at most three real zeros.

02

Step 2. Use the rational zero theorem 

As all the coefficients are integers so we use the rational zeros theorem.

The factors of the constant term 5are

p:卤1,卤5

The factors of the leading coefficient 3are

q:卤1,卤3

So, the possible rational zeros are

role="math" localid="1646191718276" pq:卤1,卤5,卤13,卤53

03

Step 3. Use the synthetic division 

Let's test the potential zero 1,

Since the remainder is not zero, it is not a factor.

04

Step 4. Finding the zero 

Now, let's test the potential zero 13 by using the synthetic division test

Since the remainder is zero, x-13is a factor.

The factor form isx-133x2-15.

05

Step 6. Use the zero product property 

As the remaining zeros satisfy the depressed equation

So,

3x2-15=03x2=15x2=5x=卤5

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Most popular questions from this chapter

Solve the inequality x2-5x鈮�24. Graph the solution set.

Find a rational function that might have the given graph.

Find the domain of the rational function.

G(x)=x-3x2+1

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f(x)=4x4-15x3-8x2+15x+4

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