forming+quadratic+equations+from+roots

Question

e.mccormick · Answer

What about it?

unklerhaukus · Answer

For a quadratic equation of the form $$y(x) =ax^2+bx+c$$
With roots $\alpha,\beta$

the sum of the roots$$\alpha+\beta=-b/a$$ and the product of the roots$$\alpha\beta=c/a$$

e.mccormick · Answer

Another way of thinking about it is that the roots are when the curve has a y of 0.... so:
$0=ax^2+bx+c$ which results in $0=(x\pm r_1)(x\pm r_2)$ as factors.  If you put things back into that factored form, you can multiply it back out.

triciaal · Answer

when you divide by a factor there is no remainder. 
if you have the roots, a and b  then (x-a) is a factor and (x-b) is a factor 
the quadratic is the product of the factors
f(x) = (x-a)(x-b)