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Chapter 4: Q. 8 (page 247)

Write a function that meets the given conditions.

Fourth-degree polynomial function with real coefficients; zeros:-2,0,3+i

Short Answer

Expert verified

The polynomial function isf(x)=x4-4x3-2x2+20x

Step by step solution

01

Step 1. Given Information

The given conditions are fourth-degree polynomial function with real coefficients; zeros:-2,0,3+i

02

Explanation

Since, the polynomial has a degree 4, the polynomial will have 4 zeroes.

Thus, 3-imust also be a zero of the function.

Use the factor theorem and distributive property to find the polynomial.

localid="1646309910774" f(x)=a(x+2)(x+0)[x-(3+i)][x-(3-i)]=ax(x+2)[x2-3x+xi-3x-xi+9-i2]=a(x2+2x)x2-6x+10=a(x4-6x3+10x2+2x3-12x2+20x)=a(x4-4x3-2x2+20x)

Leta=1then the required polynomial isx4-4x3-2x2+20x

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