polynominal with exponent of 4 question

Hello, this equation came up in class:

y^4 - 400y^2 + 25600

The teacher used this method to solve it:

let y^2 = z

z^2 - 400z + 25600

z = 320 or 80

I was just wondering what the name for the method used to solve it is, so that I can google and find out more information / practice examples etc. It is the first time I had come across this type of polynominal with an exponent higher than 3.

Thanks kindly.

Re: polynominal with exponent of 4 question

Quote:

Originally Posted by

**fran1942** Hello, this equation came up in class:

y^4 - 400y^2 + 25600

The teacher used this method to solve it:

let y^2 = z

z^2 - 400z + 25600

z = 320 or 80

I was just wondering what the name for the method used to solve it is, so that I can google and find out more information / practice examples etc. It is the first time I had come across this type of polynominal with an exponent higher than 3.

Thanks kindly.

It's just recognition that this is a quadratic equation in y^2.

By the way, the equation hasn't been solved yet. Now you need to find y.

Re: polynominal with exponent of 4 question

Quote:

Originally Posted by

**fran1942** Hello, this equation came up in class:

y^4 - 400y^2 + 25600

The teacher used this method to solve it:

let y^2 = z

z^2 - 400z + 25600

z = 320 or 80

I was just wondering what the name for the method used to solve it is, so that I can google and find out more information / practice examples etc. It is the first time I had come across this type of polynominal with an exponent higher than 3.

Thanks kindly.

These equations are known as Biquadratic Equations