# How do you find zeros of f(x)=5x^3+6x^2+x?

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Jul 11, 2017

Zeros of $f \left(x\right) = 5 {x}^{3} + 6 {x}^{2} + x$ are $0 , - 1$ and $- \frac{1}{5}$

#### Explanation:

The function $f \left(x\right) = 5 {x}^{3} + 6 {x}^{2} + x$ can be factorized as

$f \left(x\right) = x \left(5 {x}^{2} + 6 x + 1\right)$

$= x \left(5 {x}^{2} + 5 x + x + 1\right)$

$= x \left(5 x \left(x + 1\right) + 1 \left(x + 1\right)\right)$

i.e. $f \left(x\right) = x \left(5 x + 1\right) \left(x + 1\right)$

Hence zeros of $f \left(x\right) = 5 {x}^{3} + 6 {x}^{2} + x$ are $0 , - 1$ and $- \frac{1}{5}$

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