Question
Asked Oct 1, 2019
3. (a) Give the equation of a polynomial function with the indicated zeros and multiplicities.
6
multiplicity 3;
0, multiplicity 4
3, multiplicity 5;
111
(b) Find all of the rational zeros of the polynomial
p(x)=5x-18x2--3x +2
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3. (a) Give the equation of a polynomial function with the indicated zeros and multiplicities. 6 multiplicity 3; 0, multiplicity 4 3, multiplicity 5; 111 (b) Find all of the rational zeros of the polynomial p(x)=5x-18x2--3x +2

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Expert Answer

Step 1

If "a" is a zero with multiplicity k then (x-a)^k is a factor of the polynomial.

-3 has multiplicity= 5 so, (x+3)^5 is a factor.

6/11 has a multiplicity = 3 so, (x-6/11)^3 is a factor.

0 has multiplicity =4 so, (x-0)^4 =x^4 is a factor.

Step 2

We then multiply all the factors to get the polynomial.

Answer: x^4(x+3)^5 (x-(6/11))^3

6
y=(x+3)'(x-
3
4
11
Or, y=x'ox+3) (x-)
3
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6 y=(x+3)'(x- 3 4 11 Or, y=x'ox+3) (x-) 3

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Step 3

We graph the function with graphing calculator and find where it cuts the x axis.

It cuts the x axis at x= -0.4 

Or x= -2/5&nbs...

20
(-0.4, 0)
-1
C
1
2
3
4
--20
-40
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20 (-0.4, 0) -1 C 1 2 3 4 --20 -40

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