# Question regarding Polynomials

• May 2nd 2009, 10:30 PM
noobonastick
Question regarding Polynomials
Use the fourth degree equation ax^4 + bx^3 + cx^2 + dx + e = 0 whose roots are A,B,C,D to verify that

1) the equation P(x/m) = 0 has roots m times those of P(x) = 0.

Thank you.
• May 3rd 2009, 01:56 AM
CaptainBlack
Quote:

Originally Posted by noobonastick
Use the fourth degree equation ax^4 + bx^3 + cx^2 + dx + e = 0 whose roots are A,B,C,D to verify that

1) the equation P(x/m) = 0 has roots m times those of P(x) = 0.

Thank you.

Let x be a root of P(x)=0, put y=mx, then P(y/m)=P(x)=0, so mx is a root of P(x/m).

CB
• May 3rd 2009, 02:53 AM
noobonastick
Quote:

Originally Posted by CaptainBlack
Let x be a root of P(x)=0, put y=mx, then P(y/m)=P(x)=0, so mx is a root of P(x/m).

sorry I dont understand the logic... can you elaborate?
• May 3rd 2009, 09:48 AM
CaptainBlack
Quote:

Originally Posted by noobonastick
sorry I dont understand the logic... can you elaborate?

I have shown that if x is a root of P(x), then mx is a root of P(x/m).

What else do you need?

(note implicit assumption that m != 0)

CB