# What are all the zeroes of #f(x) = 2x^3 - 5x^2 + 3x - 1#?

The Real root of

#x_1 = 1/6 (5 + root(3)(44+3sqrt(177))+root(3)(44-3sqrt(177)))#

and Complex roots as below...

Given:

Then:

So:

So we want to solve:

Then using the quadratic formula:

Hence the Real root is:

and hence:

The Complex roots are:

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To find the zeroes of the function f(x) = 2x^3 - 5x^2 + 3x - 1, we set the function equal to zero and solve for x. By using methods such as factoring, synthetic division, or the rational root theorem, we can determine the roots of the polynomial equation. After finding the roots, we verify them by substituting them back into the original equation to ensure they satisfy f(x) = 0.

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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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