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Viefleur [7K]
3 years ago
14

What are the possible rational zeros of f(x) = 3x4 + x3 − 13x2 − 2x + 9?

Mathematics
1 answer:
Veronika [31]3 years ago
7 0
Rational roots theorem states that any rational root will be a factor of the constant over a factor of the leading coefficient. 
The given equation is: f(x) = 3x^4 + x^3 - 13x^2 - 2x + 9. In this case, it is a factor of 9 over a factor of 3. 

Factors of 9: ±1, ±3, ±9 
Factors of 3: ±1, ±3 

So possible rational roots are: ±1, ±3, ±9, ±1/3
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Find the zeros of the polynomial function and state the multiplicity of each.
zheka24 [161]
\bf f(x) = 4(x + 7)^2(x - 7)^3\implies 0 = 4(x + 7)^2(x - 7)^3
\\\\\\
0=(x+7)^2(x-7)^3\implies 
\begin{cases}
0=(x+7)^7\\
\qquad 0=(x+7)(x+7)\\
\qquad -7=x\\
\qquad -7=x\\
----------\\
0=(x-7)^3\\
\qquad 0=(x-7)(x-7)(x-7)\\
\qquad 7=x\\
\qquad 7=x\\
\qquad 7=x
\end{cases}

the -7 is found there twice, so it has a multiplicity of 2
the +7 is there thrice, so it has multiplicity of 3
7 0
3 years ago
What is the order from least to greatest for all three?
san4es73 [151]
21. 1/7 3/8 1/2
23. 3 5/8 3 3/8 3 1/2
25. 1/6 3/4 2/3
8 0
3 years ago
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Angela tried to solve an equation step by step. \begin{aligned} \dfrac34+m&=\dfrac54\\\\ \dfrac34+m-\dfrac34&=\dfrac54+\
Liono4ka [1.6K]

Answer:

The mistake she made was ; She didn't change the sign when subtracting -3/4 from both sides

She wrote 5/4+3/4 instead of 5/4-3/4

Step-by-step explanation:

Correct solution:

\frac{3}{4}  + m =   \frac{5}{4}

Subtract-3/4 from both sides

\frac{3}{4}  -  \frac{3}{4}  + m =  \frac{5}{4}  -  \frac{3}{4}

Simplify

m =  \frac{5}{4}  -  \frac{3}{4}  \\ m =  \frac{1}{2}

7 0
3 years ago
Find a and b so that f(x) = x^3 + ax^2 + b will have a critical point at (2,3).
Digiron [165]

Using the critical point concept, it is found that a = -3 and b = 7.

<h3>What are the critical points of a function?</h3>
  • The critical points of a function are the values of x for which:

f^{\prime}(x) = 0

In this problem, the function is:

f(x) = x^3 + ax^2 + b

Hence, the derivative is:

f^{\prime}(x) = 3x^2 + 2ax

Then:

f^{\prime}(x) = 0

3x^2 + 2ax = 0

x(3x + 2a) = 0

x = 0

3x + 2a = 0

3x = -2a

x = -\frac{2a}{3}

Since the critical point is at x = 2, we have that:

-\frac{2a}{3} = 2

-2a = 6

2a = -6

a = -3

Then:

f(x) = x^3 - 3x^2 + b

Critical point at (2,3) means that when x = 2, y = 3, then:

3 = 2^3 - 3(2)^2 + b

8 - 12 + b = 3

b = 7

You can learn more about the critical point concept at brainly.com/question/2256078

4 0
1 year ago
One day is what percent of one week?
satela [25.4K]

Answer:

1.68 hours

Step-by-step explanation:

3 0
3 years ago
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