Question

Find the sum and product of the roots of the equation 2x^2-6x+10=0

Answer 1

Sum and Product of the Roots of a Quadratic Equation

Given a quadratic equation of the form:

$x^2+mx+p=0$

It can be proven that (-m) coincides with the sum of the roots of the polynomial and p corresponds with the product of the roots.

For example, a polynomial with roots 3 and 4 has the equation:

$x^2-7x+12=0$

We are given the equation:

$2x^2-6x+10=0$

Notice the coefficient of the x squared is not 1 as required. But we can do the trick of dividing by 2:

$x^2-3x+5=0$

Now we can say:

The sum of the roots is 3

The product of the roots is 5