How do you find all the zeros of $f (x) = x^{2} + 6 x + 18$ $f(x) = x^2 + 6x + 18$ ?

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How do you find all the zeros of $f (x) = x^{2} + 6 x + 18$ $f(x) = x^2 + 6x + 18$ ?

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Answer 1 · 2016-03-10T22:49:16

Complete the square and use the difference of squares identity to find zeros:

$x = - 3 \pm 3 i$ $x = -3+-3i$

Explanation:

Complete the square then use the difference of squares identity:

$a^{2} - b^{2} = (a - b) (a + b)$ $a^2-b^2 = (a-b)(a+b)$

with $a = (x + 3)$ $a=(x+3)$ and $b = 3 i$ $b=3i$ as follows:

$f (x) = x^{2} + 6 x + 18$ $f(x) = x^2+6x+18$

$= x^{2} + 6 x + 9 + 9$ $= x^2+6x+9+9$

$= {(x + 3)}^{2} + 3^{2}$ $= (x+3)^2+3^2$

$= {(x + 3)}^{2} - {(3 i)}^{2}$ $=(x+3)^2-(3i)^2$

$= ((x + 3) - 3 i) ((x + 3) + 3 i)$ $= ((x+3)-3i)((x+3)+3i)$

$= (x + 3 - 3 i) (x + 3 + 3 i)$ $= (x+3-3i)(x+3+3i)$

Hence $f (x) = 0$ $f(x) = 0$ when $x = - 3 \pm 3 i$ $x=-3+-3i$

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How do you find all the zeros of $f (x) = x^{2} + 6 x + 18$ $f(x) = x^2 + 6x + 18$ ?

1 Answer

Explanation:

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How do you find all the zeros of f(x)=x2+6x+18f(x) = x^2 + 6x + 18?

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How do you find all the zeros of $f (x) = x^{2} + 6 x + 18$ $f(x) = x^2 + 6x + 18$ ?