# 3. (a) Give the equation of a polynomial function with the indicated zeros and multiplicities.6multiplicity 3;0, multiplicity 43, multiplicity 5;111(b) Find all of the rational zeros of the polynomialp(x)=5x-18x2--3x +2

Question help_outlineImage Transcriptionclose3. (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 fullscreen
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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.

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...

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