1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
eimsori [14]
10 months ago
11

Solve the equation: 2x^3-5x^2-6x+9=0 given that x=1 is a zero

Mathematics
1 answer:
olga_2 [115]10 months ago
7 0

The given function

2x^3+5x^2-6x+9=0

Since x = 1 is one of its zeroes, then we will use it to find the other zeroes

\begin{gathered} x=1 \\ x-1=1-1 \\ x-1=0 \end{gathered}

The factor is x - 1

Use the long division to find the other factors

\frac{2x^3-5x^2-6x+9}{x-1}

Divide 2x^3 by x, then multiply the answer by (x - 1)

\begin{gathered} \frac{2x^3}{x}=2x^2 \\ 2x^2(x-1)=2x^3-2x^2 \end{gathered}

Subtract the product from the original equation

\begin{gathered} 2x^3-5x^2-6x+9-(2x^3-2x^2)= \\ (2x^3-2x^3)+(-5x^2+2x^2)-6x+9= \\ 0-3x^2-6x+9 \\ \frac{2x^3-5x^2-6x+9}{x-1}=2x^2+\frac{-3x^2-6x+9}{x-1} \end{gathered}

Now, divide -3x^2 by x, then multiply the answer by (x - 1)

\begin{gathered} -\frac{3x^2}{x}=-3x \\ -3x(x-1)=-3x^2+3x \end{gathered}

Subtract it from the denominator of the fraction

\begin{gathered} (-3x^2-6x+9)-(-3x^2+3x)= \\ (-3x^2+3x^2)+(-6x-3x)+9= \\ 0-9x+9 \\ \frac{2x^2-5x^2-6x+9}{x-1}=2x^2-3x+\frac{-9x+9}{x-1} \end{gathered}

Divide -9x by x and multiply the answer by (x - 1)

\begin{gathered} \frac{-9x}{x}=-9 \\ -9(x-1)=-9x+9 \end{gathered}

Subtract it from the numerator

\begin{gathered} -9x+9-(-9x+9)= \\ (-9x+9x)+(9-9)= \\ 0+0 \\ \frac{2x^3-5x^2-6x+9}{x-1}=2x^2-3x-9 \end{gathered}

Then we will factor this trinomial into 2 factors

\begin{gathered} 2x^2=(2x)(x) \\ -9=(-3)(3) \\ (2x)(-3)+(x)(3)=-6x+3x=-3x\rightarrow middle\text{ term} \\ 2x^2-3x^2-9=(2x+3)(x-3) \end{gathered}

Equate each factor by 0 to find the other zeroes of the equation

\begin{gathered} 2x+3=0 \\ 2x+3-3=0-3 \\ 2x=-3 \\ \frac{2x}{2}=\frac{-3}{2} \\ x=-\frac{3}{2} \end{gathered}\begin{gathered} x-3=0 \\ x-3+3=0+3 \\ x=3 \end{gathered}

The zeroes of the equations are 1, 3, -3/2

The solutions of the equations are

\begin{gathered} x=-\frac{3}{2} \\ x=1 \\ x=3 \end{gathered}

You might be interested in
Is it true that square roots can be compared and ordered by comparing and ordering the numbers underneath the radical symbol?
Naddik [55]

Answer:

Yes

Step-by-step explanation:

I had this same question on a quiz and it is correct!

6 0
3 years ago
Which expression is equivalent to g5?
zaharov [31]

Answer:

9 x 9 x 9 x 9 x 9

Step-by-step explanation:

9^5 = 9 x 9 x 9 x 9 x 9

7 0
3 years ago
What is angle m 2 ? What is angle m 1?
mezya [45]

Answer:

Angle measure two is equal to 75º and Angle measure one is equal to 105º

Step-by-step explanation:

I know this because angle one is alternate exterior angle with angle 7 and angle seven forms a staight line with angle 75 so to find angle 7 you have to do 180-75 and that would equal 105.

for angle two it is interior angles with angle 75 so this means that are congruent angles which means they both have the same measure

7 0
3 years ago
Which graph shows the solution to the system of linear inequalities?<br> y&lt; 2x-5<br> y&gt;-3x + 1
trapecia [35]

Answer:

See explanation

Step-by-step explanation:

Plot the solution sets to both inequalities.

1. For the inequality y First, plot the dotted line y=2x+5 (dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.

2\cdot 0-5=-5

so the origin does not belong to the needed part. Shade the part, which does not include origin.

2. For the inequality y>-3x+1. First, plot the dotted line y=-3x+1 (dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.

-3\cdot 0+1=1>0

so the origin does not belong to the needed part. Shade the part, which does not include origin.

3. Find the common region of these two shaded parts - this is the solution to the system of two inequalities.

5 0
3 years ago
Students are making ornaments and each takes 1 2 of a piece of Bristol board. They go to the cupboard and find 1 1 2 pieces of B
s2008m [1.1K]

Answer: 3

Step-by-step explanation:

Feom the question, we are informed that students are making ornaments and each takes 1/2 of a piece of Bristol board and that they go to the cupboard and find 1 1/2 pieces of Bristol board.

The number of ornaments that they can make will be calculated by dividing 1 1/2 by 1/2. This will be:

= 1 1/2 ÷ 1/2

= 3/2 ÷ 1/2

= 3/2 × 2/1

= 3

They can make 3 ornaments

8 0
2 years ago
Other questions:
  • You have a handful of quarters, nickels, and dimes that totals 75 cents. Make a table listing all the possible combinations. How
    15·1 answer
  • Use substitution to solve each of the following pairs of simultaneous equations for x and y in terms of m and n.
    14·1 answer
  • 1) 4x - 3y=3<br>x+3y= 12​
    9·2 answers
  • |60| ___ |-60|<br><br> =<br> &lt;<br> &gt;
    7·2 answers
  • Is 0.3 greater that 0.15
    7·2 answers
  • Maths question pls answer
    9·2 answers
  • Solve for x please help
    14·1 answer
  • If Kate is 14, what was her age x years ago?
    5·1 answer
  • What is the greatest common factor of 42 and 15?
    5·2 answers
  • Good Luck! Try your best!
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!