Write a polynomial function f of least degree

Answered question

2022-01-19

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the polynomial in standard form. 2, 3+2i, sqrt 5

Answer & Explanation

xleb123

xleb123

Skilled2022-01-30Added 181 answers

f(x)=(x2)(x5)(x+5)(x(3+2i))(x+(3+2i))

=ddx((x2)(x5)(x+5)(x32i)(x+3+2i))

Apply the Product Rule (fg)=fg+fg

f=x2,g=(x5)(x+5)(x32i)(x+3+2i)

=ddx(x2)(x5)(x+5)(x32i)(x+3+2i)+ddx((x5)(x+5)(x32i)(x+3+2i))(x2)

ddx(x2)=1

ddx((x5)(x+5)(x32i)(x+3+2i))=(4x320x)24ix

=1(x5)(x+5)(x32i)(x+3+2i)+(4x320x24ix)(x2)

1·(x5)(x+5)(x32i)(x+3+2i)+(4x320x24ix)(x2):(5x48x330x2+40x+25)+i(6036x2+48x)

=(5x48x330x2+40x+25)+i(6036x2+48x)

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