Question

If 2x^3 + ax^2 + bx - 6 has x-1 as a factor and leaves a remainder 2 when divided by (x-2) , find the value of "a" and "b" .

Answer 1

F(x) = 2x^3 + ax ^2 + bx - 6 ....(1)

if x -1 is a factor of f(x) .. then f(1) = 0

--->2× (1)3 + a(1)2 + b(1) - 6 = 0

---> a + b = 4 ...... (2)...

and as f(x) on division wid x - 2 leaves a remainder of 2

---> f(2) = 2

2×8+a×4+b2-6=2

---> 4a+2b= -8 .... (3)....

From (2)&(3)

a = -8 and b =12