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O POLYNOMIAL AND RATIONAL FUNCTIONSFinding a polynomial of a given degree with given zeros: Comple...Find a polynomial f(x) of degree 3 with real coefficients and the following zeros.-2, 2if(x)

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O POLYNOMIAL AND RATIONAL FUNCTIONS
Finding a polynomial of a given degree with given zeros: Comple...
Find a polynomial f(x) of degree 3 with real coefficients and the following zeros.
-2, 2i
f(x)
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O POLYNOMIAL AND RATIONAL FUNCTIONS Finding a polynomial of a given degree with given zeros: Comple... Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. -2, 2i f(x)

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Step 1

We know that if a+ib is zero of a polynomial, then a-ib is also its polynomial. So, zeros of the required polynomial are -2,2i,-2i

Step 2

Thus the polynomial has facto...

P(x)(x+2)x-21)(x+2i
p(x) (x+2)(x-4)
p(x)(x2)x +4)
P(x) x(x +4)+2(x+4)
p(x) x 4x+2x 8
p(x)x2x24x +8
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P(x)(x+2)x-21)(x+2i p(x) (x+2)(x-4) p(x)(x2)x +4) P(x) x(x +4)+2(x+4) p(x) x 4x+2x 8 p(x)x2x24x +8

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