Explained: "Find all zeros of the polynomial. P(x)=x3+7x2+18x+18"

Secondary
Algebra
Algebra II
Polynomial factorization

prsategazd

Answered question

2021-12-13

Find all zeros of the polynomial.

P (x) = x^{3} + 7 x^{2} + 18 x + 18

Answer & Explanation

temnimam2

Beginner2021-12-14Added 36 answers

Step 1
Given polynomial

P (x) = x^{3} + 7 x^{2} + 18 x + 18

Step 2
Zeros of the polynomial

x^{3} + 7 x^{2} + 18 x + 18 = 0

x^{3} + 3 x^{2} + 4 x^{2} + 12 x + 6 x + 18 = 0

x^{2} (x + 3) + 4 x (x + 3) + 6 (x + 3) = 0

(x + 3) (x^{2} + 4 x + 6) = 0

x=-3 and

x^{2} + 4 x + 6 = 0

Now,

x^{2} + 4 x + 6 = 0

x = \frac{- 4 \pm \sqrt{4^{2} - 4 \times 1 \times 6}}{2}

x = \frac{- 4 \pm \sqrt{- 8}}{2}

x = \frac{- 4 \pm 2 \sqrt{- 2}}{2}

x = - 2 \pm \sqrt{- 2}

x = - 2 \pm \sqrt{2} i

Hence,
zeros are
x=-3

x = - 2 + \sqrt{2} i

x = - 2 - \sqrt{2} i

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