Find the sum and the product of the roots of the equation: x^2+35x−51=0

The first step will be to find the roots of the equation:

x^2 + 35*x - 51 = 0.

We know that for a quadratic equation like:

a*x^2 + b*x + c = 0

The solutions are:

In this case we have:

a = 1

b = 35

c = -51

Then the solutions are:

Then the two solutions are:

x1 = (-35 + √(1429))/2

x2 = (-35 - √(1429))/2

The sum will be:

S = x1 + x2 =  (-35 + √(1429))/2 + (-35 - √(1429))/2

                  = (-35 + √(1429) - 35 - √(1429))/2 = -35

The product will be:

P = x1*x2 = ( (-35 + √(1429))/2)*( (-35 - √(1429))/2)

                = (-35 + √(1429))*(-35 - √(1429))/4

                = (35*√(1429) + 35^2 + 1429 - 35*√(1429))/4

                = (1225 + 1429)/4 = 663.5