How Do You Solve: Finding A Polynomial of Minimum Degree

[grace]

How do you solve these problems?

Find a polynomial of minimum degree (there are many) that have the given zeros.


1) -2, 0, 5, 6

Make the leading coefficient equal to 1:

f (x)=


2) 1 - square root of 5 and 1 + square root of 5

Make the leading coefficient equal to 1 and eliminate the parentheses:

f (x) =


Please help. Thanks.

 

[pka]

Here is #1 free of charge.
\(\displaystyle \L\left( {x + 2} \right)\left( x \right)\left( {x - 5} \right)\left( {x - 6} \right)\)

 

[skeeter]

How do you solve these problems?

Find a polynomial of minimum degree (there are many) that have the given zeros.


1) -2, 0, 5, 6

Make the leading coefficient equal to 1:

f (x) = \(\displaystyle (x + 2)(x - 0)(x - 5)(x - 6)\)


2) 1 - square root of 5 and 1 + square root of 5

Make the leading coefficient equal to 1 and eliminate the parentheses:

f (x) = \(\displaystyle [x - (1 - \sqrt{5})][x - (1 + \sqrt{5})]\)


Please help. Thanks.