<p>How to you find the sum of zeros or product of zeros by just looking at the quadratic equation? I know there is some type of ratio (-b/a? or something like that) but I can’t remember it.</p>
<p>Given a quadratic equation with roots t and r, we can write the equation as:
(x-t)(x-r) [do you see why?]
We can then foil this out to get
x^2 -tx-rx+tr
Simplify to
x^2-(t+r)x+tr
Therefore the sum of the roots would be -1 times the coefficient of the x term and the product of the roots is the term without an x or x^2 term in the quadratic equation.</p>
<p>Ex: If given the quadratic equation defined as
x^2+7x+14
The sum of the roots is -7 and the product of the roots is 14</p>
<p>Note: This only works if the coefficient of the x^2 term is 1.</p>
<p>If the coefficient of the x^2 term is not 1 we can do a little more work to figure it out:
We write the quadratic equation as:
ax^2 + bx + c
To get the x^2 coefficient to be 1, we can divide everything by a
x^2 + b/ax + c/a</p>
<p>So, by our earlier definition, the sum of the roots is
-b/a
And the product of the roots is
c/a</p>
<p>Ex: If we have the quadratic equation defined by
4x^2 + 3x + 17
The sum of the roots is -3/4
The product of the roots is 17/4</p>
<p>(-1)^k * (a<em>{n-k}) = sum of product of the roots taken k at a time, where a</em>(n) is the coefficient of the x^n term.</p>