# Polynomial Roots

• September 23rd 2010, 08:58 PM
asaver
Polynomial Roots
Just a quick question;
Just say you had a linear equation which was one of the roots of a polynomial (quadratic). Lets say y=2x+2. How would the gradient of the second linear equation affect the polynomial?
I just cant seem to put it in words/make it sound mathematically convincing.
Thanks
• September 23rd 2010, 10:26 PM
undefined
Quote:

Originally Posted by asaver
Just a quick question;
Just say you had a linear equation which was one of the roots of a polynomial (quadratic). Lets say y=2x+2. How would the gradient of the second linear equation affect the polynomial?
I just cant seem to put it in words/make it sound mathematically convincing.
Thanks

A polynomial $P(x)=ax^2+bx+c$ with $a\ne0$ has exactly two complex roots and at most two real roots; calling a root a linear equation makes no sense to me.
• September 23rd 2010, 10:32 PM
TheCoffeeMachine
Quote:

Originally Posted by asaver
Just a quick question;
Just say you had a linear equation which was one of the roots of a polynomial (quadratic). Lets say y=2x+2. How would the gradient of the second linear equation affect the polynomial?

Do you mean $2x+2$ is a factor of the quadratic (i.e., $x = -1$ is a root)?
• September 24th 2010, 12:11 AM
asaver
yeah, thats what i meant. sorry for my misuse of terms.
• September 24th 2010, 12:20 AM
mr fantastic
Quote:

Originally Posted by asaver
yeah, thats what i meant. sorry for my misuse of terms.

You're asking what the effect of a is in the parabola y = (2x + 2)(ax + b) ....? Do you mean from a transformation point of view? Please be more specific in what yuo are trying to find.