There is a certain question in which the sum of the solutions (roots) of a quadratic equation is given which is 47, as well as the product of solutions, which is -59. The formulas for the sum and product of two real distinct roots are:
x1 + x2 = -b / a
x1 * x2 = c / a
Also, the question recommended using:
x1^2 + x2^2 = (b^2 - 2*a*c) / a^2
After using,:
47 = -b / a
b = -47*a
And,:
59 = c / a
c = -59*a
Substituting these into:
x1^2 + x2^2 = (b^2 - 2*a*c) / a^2
I get:
2327 = x1^2 + x2^2
Now, I have:
x1 + x2 = 47
x1 * x2 = -59
x1^2 + x2^2 = 2327
I am not sure what to do next, to get the values of a, b, c. I tried substituting different equations into others but there was no result in isolating for variable and getting its value. I was wondering what next steps I should take to isolate and get the values of a, b, and c for the quadratic equation. Thanks.
The answer is standard: two numbers $x_1, x_2$ with a sum $s$ and product $p$ are the roots of the quadratic equation $$(x-x_1)(x-x_2)=x^2-sx+p=0. $$