# How do you solve #x^3-3x+1=0# using Cadano's method ?

Here's an alternative method...

Given:

Here's an alternative trigonometric sustitution method of solution, suitable for cubics such as this one, with three real zeros (Cardano's "casus irreducibilis"):

Consider the substitution:

Then our cubic equation becomes:

Hence:

Hence:

So:

So:

which results in distinct values:

By signing up, you agree to our Terms of Service and Privacy Policy

See explanation...

As a result, if we attempt to solve using Cardano's method then the solution will be expressed in terms of irreducible cube roots of complex numbers - Cardano's "casus irreducibilis".

Let's go ahead anyway to see it happen...

Given:

Then:

which expands to:

By signing up, you agree to our Terms of Service and Privacy Policy

To solve ( x^3 - 3x + 1 = 0 ) using Cardano's method, first let ( x = u + v ). Then, substitute this into the equation and expand. This will yield a cubic equation in terms of ( u ) and ( v ). Choose ( u ) and ( v ) such that the second degree term vanishes. Then solve the quadratic equations for ( u ) and ( v ). Once you find the values of ( u ) and ( v ), substitute them back into ( x = u + v ) to obtain the solutions for ( x ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- How do you find the zeros of # 4x^4 + 3x^3 + 2x^2 - 3x + 4#?
- How do you write a polynomial equation of least degree given the roots -1, 1, 4, -4, 5?
- How do you describe the end behavior for #f(x)=x^4-x^2-2#?
- How do you use the intermediate value theorem to verify that there is a zero in the interval [0,1] for #h(theta)=1+theta-3tantheta#?
- How do you write the polynomial function with the least degree and zeroes i, 2 - √3?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7