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MatroZZZ [7]
3 years ago
8

Write a third degree polynomial function y = P(x) with rational coefficients so that P(x) = 0 has roots -2 and 6 + i

Mathematics
1 answer:
Vanyuwa [196]3 years ago
7 0

Answer:P(x)=x^3-10x^2+13x+74


Step-by-step explanation: We are given roots of a third degree polynomial function -2, 6+i.

Note: a radical always comes with pair of plus and minus sign.

Therefore, there would be one more root 6-i.

So, all the roots would be -2, 6+i, 6-i.

So, the factors of polynomial function would be

(x+2)(x-6-i)(x-6+i)

Multiplying those factors,

(x+2)(x^2-6x+xi -6x+36-6i-ix+6i-i^2)

(x+2)(x^2-12x+36+1)

(x+2)(x^2-12x+37)

x^3-12x^2+2x^2+37x-24x+74

=x^3-10x^2+13x+74

Therefore,

P(x)=x^3-10x^2+13x+74




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3 years ago
∆JKL~∆MNO and J/K MN =2/3 find the length of NO if KL=12.
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Step-by-step explanation:

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Solution:

Δ JKL ~ Δ LMN ….{Given)

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