Question

Find all zeros of the polynomial function given below.5x^5-51x^4+155x^3-229x^2+540x-100

Find all zeros of the polynomial function given below.5x^5-51x^4+155x^3-229x^2+540x-100

Math   Precalculus   
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Homework Answers

Answer #1

Given polynomial is,

5x5​​​​​​ - 51x4​​​​​​ + 155x3​​​​​​ - 229x2​​​​​​ + 540x - 100

=5x5​​​​​​ - x4​​​​​​ - 50x4 + 10x3​​​ + 145x3 - 29x2​​​​​​ - 200x2 + 40x + 500x - 100

= x4(5x - 1) - 10x3​​​​​​(5x - 1) + 29x2(5x - 1) - 40x(5x - 1) + 100(5x - 1)

= (5x - 1)(x4​​​​​​ - 10x3​​​​​​ + 29x2​​​​​​ - 40x + 100)

= (5x - 1)(x4​​​​​​ + 4x2​​​​​​ - 10x3 - 40x + 25x2​​​ + 100)

= (5x - 1){ x2(x2​​​​​​ + 4) - 10x(x2​​​​​​ + 4) + 25(x2​​​​​​ + 4) }

= (5x - 1)(x2​​​​​​ + 4)(x2​​​​​​ - 10x + 25)

= (5x - 1)(x2​​​​​​ + 4)(x - 5)2

So zeros of the given polynomial are,

(1/5), -2i, 2i, 5

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