Question

forming+quadratic+equations+from+roots

Answer 1

What about it?

Answer 2

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\[\alpha\beta=c/a\]

Answer 3

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.

Answer 4

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)