# How do you find all rational roots for #8y^4 - 6y^3 + 17y^2 - 12y + 2 = 0#?

The rational roots are

The remaining two roots are

That means that the only possible rational zeros are:

We find:

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The rational root theorem states that any rational root of a polynomial equation (a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0 = 0) must be of the form ( \pm \frac{p}{q} ), where (p) is a factor of the constant term (a_0) and (q) is a factor of the leading coefficient (a_n).

For the equation (8y^4 - 6y^3 + 17y^2 - 12y + 2 = 0), the constant term is 2 and the leading coefficient is 8.

The factors of 2 are ±1, ±2, and the factors of 8 are ±1, ±2, ±4, ±8.

Therefore, the possible rational roots are:

±1, ±2, ±1/2, ±1/4

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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