If B and C are the real roots of x^2 +Bx + C = 0, where B and C are not zeros

If B and C are the real roots of x^2 + Bx + C = 0, where B and C are not zeros, find the values of B and C.

Write a polynomial with the given roots and solve by comparing coefficients:
x² + Bx + C = (x - B)(x - C)
x² + Bx + C = x² - Cx - Bx + BC
x² + Bx + C = x² - (B + C)x + BC
BC = C
B = 1
B + C = -B
C = -2B
C = -2
y = x² + x - 2

use the Viete formular, you have: B+C = - B and B.C = C. Thus B = 1 and C = -2.
Because B is positive and C is negative, the equation has two real roots.