Thread: quadratic function

How do you show that in the quadratic function: ax^2 + bx + c with 2 roots x1 and x2 that:

1) x1 + x2 = -b/a

and

2) x1*x2 = c/a

?

Originally Posted by JQ2009

How do you show that in the quadratic function: ax^2 + bx + c with 2 roots x1 and x2 that:

1) x1 + x2 = -b/a

and

2) x1*x2 = c/a

?

Use the fact that . What happens when you add up the two possible answers?

Originally Posted by JQ2009

Let

and

Then calculate


Alternatively:

Spoiler:

If and are the roots of the equation , then the equation must be of the form

for some constant .

Therefore, we have:






Equating the coefficients of x gives:


But , so:

Originally Posted by JQ2009

Let

and

Then calculate

Alternatively:

Spoiler:

If and are the roots of the equation , then the equation must be of the form

for some constant .

Therefore, we have:






Equating the constants gives:


But , so:

then you can plug in the values for a, b and c