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Find a polynomial with the following zeros.

HELPPPP ASAPPP

Find a polynomial with the following zeros. HELPPPP ASAPPP-example-1
User James Alvarez
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1 Answer

18 votes
18 votes

Answer:

x³ - 4x² + 2x + 4 = 0

Here's how I solved this:

You start off by rewriting the zeros into factors:

1 - √3 → x = 1 - √3 → (x - 1 - √3)

2 → x = 2 → (x - 2)

1 + √3 → x = 1 + √3 → (x - 1 + √3)

Now you want to multiply the factors together:

(x - 1 - √3) · (x - 2) · (x - 1 + √3)

- Multiply the first two factors together -

(x - 1 - √3) · (x - 2)

(x · x - x · 2 - √3 · x + √3 · 2 - x + 2)

- Combine like terms and simplify -

(x · x - x · 2 - √3 · x + √3 · 2 - x + 2)

(x² - 3x - √3 · x + 2√3 + 2)

- Now multiply the third factor -

(x² - 3x - √3 · x + 2√3 + 2)(x - 1 + √3)

(x² · x + x² · √3 - x² - 3x · x - 3x · √3 + 3x - √3 · xx - √3 · x · √3 +√3 · x + 2 · √3 · x + 2 · √3 · √3 - 2 · √3 + 2x + 2 · √3 - 2)

(x³ + x² · √3 - x² - 3x² - 3x · √3 + 3x - √3 + 3x - √3 * x² - x · 3 + √3 · x + 2 · √3 · x + 2 · 3 - 2 × √3 + 2x + 2 √3 - 2)

- Combine like terms and simplify -

(x³ + x² · √3 - x² - 3x² - 3x · √3 + 3x - √3 + 3x - √3 * x² - x · 3 + √3 · x + 2 · √3 · x + 2 · 3 - 2 × √3 + 2x + 2 √3 - 2)

x³ - 4x² + 2x + 4

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And there we get our solution: x³ - 4x² + 2x + 4

User Subes
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