Find the zeroes of $ x^{2}+2 x+4 $.

Given: 

Given polynomial is \( x^{2}+2 x+4 \). 

To do: 

We have to find the zeroes of the given polynomial.

Solution:

Let $p(x)=x^{2}+2 x+4$

To find the zeroes of the given polynomial we have to equate it to zero.

Therefore,

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

$\Rightarrow x^2+2x+4=0$

$\Rightarrow x=\frac{-2 \pm \sqrt{2^2-4\times1\times4}}{2\times1}$

$=\frac{-2 \pm \sqrt{4-16}}{2\times1}$

$=\frac{-2 \pm \sqrt{-12}}{2}$

$=\frac{-2 \pm \sqrt{-4\times3}}{2}$

$=\frac{-2 \pm 2\sqrt{-3}}{2}$

$=-1 \pm \sqrt{3} i$

The zeroes of the given polynomial are $-1+\sqrt{3} i$ and $-1-\sqrt3 i$.

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Updated on: 10-Oct-2022

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