+452 The roots of Ax^2+Bx+1 are the same as the roots of x^2- 3x + 5 + x^2 - 2x + 1. What is A+B?
+130462 x^2 -4x + 5 + x^2 -2x + 1 = 0
(x -1 ) (x + 5) + (x -1)^2 = 0
(x -1) [ ( x + 5) + (x -1) ] = 0
(x -1) [ 2x + 4] = 0
x -1 = 0 2x + 4 = 0
x = 1 x = -2
Sum of the roots = -B /A
-2 + 1 = - B / A
-1 = -B / A
1 = B/A
A = B
Product of the Roots = C/A
-2 * 1 = C/A =1/A
-2 = 1/A
-2A = 1
A = -1/2
B = -1/2
A + B = -1/2 + -1/2 = -1
