# Solving cubic equations using calculator

#### Hawk

Hello everyone,
I have a polynomial Equation I want to solve using my Texas Ti-82. I have tried using (Math- Solve) and I get the first root. how can I get the 2nd and 3rd roots too?

Kind Regards

#### skeeter

Math Team
why not just graph the polynomial setting the proper window for x-min and x-max to see the zeros, then use the zero function located on the calculate menu ... ?

• topsquark

#### Hawk

That's a way but I don't use graphic solutions. I am working with vibrations and dynamic behavior of materials so its more convenient for me to get the roots as numbers directly. Thanks for your answer btw.

#### skeeter

Math Team
If you're looking for numerical roots, try wolfram alpha's equation solver ...

• topsquark

#### Hawk

Thank you very much I got the answer but I would really appreciate if someone could explain how to do it using Texas IT-82 since I'm going to have exam and the only allowed tool is calculator.

#### skeeter

Math Team
Can you provide a specific example of a polynomial equation that you want to see solved with a TI ?

#### skipjack

Forum Staff
If the equation is f(x) = 0, and the calculator tells you that x = r is a solution, calculate the coefficients of the quadratic polynomial g(x) = f(x)/(x- r), then solve g(x) = 0.

• topsquark

#### mathman

Forum Staff
If you have one root of a cubic, you can obtain the quadratic for the other two roots by synthetic division of the the cubic by the linear factor of the root you got.

#### Hawk

Can you provide a specific example of a polynomial equation that you want to see solved with a TI ?
This polynomial equation below, I solved using TI-82 and I only got one root:
$$\displaystyle 4x^3-16000x^2+16*10^6x-3072*10^3=0$$
so got the first root as 250. How do I find the other ones, or use this root to find out other ones?

#### Hawk

If the equation is f(x) = 0, and the calculator tells you that x = r is a solution, calculate the coefficients of the quadratic polynomial g(x) = f(x)/(x- r), then solve g(x) = 0.
I didn't get that how to apply that.