prsategazd

2021-12-13

Find all zeros of the polynomial.

$P\left(x\right)={x}^{3}+7{x}^{2}+18x+18$

temnimam2

Beginner2021-12-14Added 36 answers

Step 1

Given polynomial

$P\left(x\right)={x}^{3}+7{x}^{2}+18x+18$

Step 2

Zeros of the polynomial

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

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

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

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

x=-3 and${x}^{2}+4x+6=0$

Now,

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

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

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

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

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

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

Hence,

zeros are

x=-3

$x=-2+\sqrt{2}i$

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

Given polynomial

Step 2

Zeros of the polynomial

x=-3 and

Now,

Hence,

zeros are

x=-3