SOLUTION: Write a polynomial function P(x) with rational coefficients so that P(x)=0 has the given roots.
1. -6,3, and -15i
2. 4+√5 and 8i
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Question 1032204: Write a polynomial function P(x) with rational coefficients so that P(x)=0 has the given roots.
1. -6,3, and -15i
2. 4+√5 and 8i
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Write a polynomial function P(x) with rational coefficients so that P(x)=0 has the given roots.
1. -6,3, and -15i ; add 15i to the lineup
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P(x) = a(x+6)(x-3)(x+15i)(x-15i)
= a(x+6)(x-3)(x^2+226)
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2. 4+√5 and 8i ; add 4-sqrt(t) and -8i to the lineup
P(x) = a(x-4-sqrt(5))(x-4+sqrt(5)(x-8i)(x+8i)
= a((x-4)^2-5)(x^2+64)
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Cheers,
Stan H.
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