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andrew11 [14]
3 years ago
5

Write a polynomial function in standard form with the given zeros 1, -1, -4

Mathematics
1 answer:
Reil [10]3 years ago
4 0

since its the zeros it should be x -/+ something

(x-1)(x+1)(x+4)

multiply for standard form

((x^2)-1)(x+4)

x^3-x

+    x^2 -4

x^2 + x^2 -x -4

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use\ Vieta's\ formula:\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}=\frac{\alpha^2+2\alpha\beta+\beta^2-2\alpha\beta}{\alpha\beta}=\frac{(\alpha+\beta)^2-2\alpha\beta}{\alpha\beta}=\frac{(\alpha+\beta)^2}{\alpha\beta}-2\\\\\alpha+\beta=\frac{-b}{a};\ \alpha\beta=\frac{c}{a}\\\\\frac{(\alpha+\beta)^2}{\alpha\beta}-2=\frac{\left(\frac{-b}{a}\right)^2}{\frac{c}{a}}-2=\frac{b^2}{a^2}\cdot\frac{a}{c}-2=\frac{b^2}{ac}-2

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