# Polynomial Roots

• Sep 23rd 2010, 07:58 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
• Sep 23rd 2010, 09:26 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 \$\displaystyle P(x)=ax^2+bx+c\$ with \$\displaystyle a\ne0\$ has exactly two complex roots and at most two real roots; calling a root a linear equation makes no sense to me.
• Sep 23rd 2010, 09:32 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 \$\displaystyle 2x+2\$ is a factor of the quadratic (i.e., \$\displaystyle x = -1\$ is a root)?
• Sep 23rd 2010, 11:11 PM
asaver
yeah, thats what i meant. sorry for my misuse of terms.
• Sep 23rd 2010, 11:20 PM
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.