Answer:
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:
[tex]x = \frac{-b +- \sqrt{b^2 - 4*a*c} }{2*a}[/tex]
In this case we have:
a = 1
b = 35
c = -51
Then the solutions are:
[tex]x = \frac{-35 +- \sqrt{(-35)^2 - 4*1*(-51)} }{2*1} = \frac{-35 +- \sqrt{1429} }{2}[/tex]
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
