What is the value of b+c, when x^2+bx+c > 0 only when x E (-infty, -2) U (3,infty)?
+9466 There is probably a better way to do this but here's one way....
x2 + bx + c > 0 for x in the interval (-∞, -2) U (3, ∞)
This implies that x2 + bx + c = 0 when x = -2 and when x = 3
The equation of a parabola with zeros at -2 and 3 is
y = a(x + 2)(x - 3)
y = a(x2 - x - 6)
y = ax2 - ax - 6a
Since the coefficient of x2 in x2 + bx + c is 1 then a = 1
x2 + bx + c = x2 - x - 6
b = -1 and c = -6
b + c = -1 + -6 = -7
+9466 There is probably a better way to do this but here's one way....
x2 + bx + c > 0 for x in the interval (-∞, -2) U (3, ∞)
This implies that x2 + bx + c = 0 when x = -2 and when x = 3
The equation of a parabola with zeros at -2 and 3 is
y = a(x + 2)(x - 3)
y = a(x2 - x - 6)
y = ax2 - ax - 6a
Since the coefficient of x2 in x2 + bx + c is 1 then a = 1
x2 + bx + c = x2 - x - 6
b = -1 and c = -6
b + c = -1 + -6 = -7
