How do you find all the roots of $f (x) = 3 x^{2} + 18 x + 27$ $f(x) = 3x^2 + 18x + 27$ ?

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How do you find all the roots of $f (x) = 3 x^{2} + 18 x + 27$ $f(x) = 3x^2 + 18x + 27$ ?

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Answer 1 · 2016-08-13T23:12:10

$f (x)$ $f(x)$ has zero $x = - 3$ $x=-3$ of multiplicity $2$ $2$

Explanation:

$f (x) = 3 x^{2} + 18 x + 27$ $f(x) = 3x^2+18x+27$

$= 3 (x^{2} + 6 x + 9)$ $=3(x^2+6x+9)$

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

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

So the zeros of $f (x)$ $f(x)$ are both $- 3$ $-3$ , i.e. $x = - 3$ $x=-3$ is a zero with multiplicity $2$ $2$ .

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How do you find all the roots of $f (x) = 3 x^{2} + 18 x + 27$ $f(x) = 3x^2 + 18x + 27$ ?

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Explanation:

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How do you find all the roots of f(x) = 3x^2 + 18x + 27f(x)=3x2+18x+27f(x) = 3x^2 + 18x + 27?

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How do you find all the roots of $f (x) = 3 x^{2} + 18 x + 27$ $f(x) = 3x^2 + 18x + 27$ ?