Sum of roots and product of roots?

Question

How do you find them?

Answer 1

if there is an equation of the form

ax^2 +bx + c =0

bring it to the form by dividing by a,

x^2 + (b/a)x + c/a =0

if h & k are the two roots;

then,
Sum of roots= h+k= -b/a

Product of roots= h*k= c/a

Useful Hint:

if D=discriminant= b^2-4ac

then,

Difference of roots = h-k = √D / a

[ Most people (esp. teachers) don't know this ]

Answer 2

If ax^2 + bx + c = 0 is a given quadratic equation,
sum of the roots = - b/a and
product of the roots = c/a.

Example: 3x^2 + 4x + 5 = 0
sum of the roots = - 4/3 and
product of the roots = 5/3.

Answer 3

For

ax^2+bx+c=0

the sum of the roots = x1+x2=-b/2a

the product of the roots = x1*x2=c/a

Answer 4

The idea is to compare coefficients of like terms.

For example,
Let r1 and r2 be the two roots.
x^2 + 4x + 10 = (x-r1)(x-r2) = x^2 - (r1+r2)x + r1r2 = 0
Compare coefficients,
the sum of the roots = r1+r2 = -4
the product of the roots = r1r2 = 10