If a + b + 4 and a^3 + b^3 = 44, then a, b are the roots of which quadratic equation?
+129907 a + b = 4
(a + b)^2 = 16
a^2 + 2ab + b^2 = 16
a^2 + b^2 = 16 - 2ab
a^3 + b^3 = ( a + b) ( a^2 - ab + b^2) =
44 = ( 4) ( 16 - 2ab - ab)
44/4 = 16 - 3ab
11 = 16 - 3ab
3ab = 16 - 11
3ab = 5
ab = 5/3
In the form ax^2 + bx + c
a = 3
c = 5
The sum of the roots = 4 = -b/a
So
4 = -b/ 3
12 = -b
-12 = b
The quadratic is 3x^2 - 12x + 5
