Question

If x-2 is a factor of x3 +ax2+bx+16 and a-b=6.find the value of a and b

Answer 1

a value is -2

b value is -8

Answer 2

x-2 is the factor then it must be in the form of
x- (+2) so +2 is the zero of the given polynomial
:. f(x) = x^3 + ax^2 + bx + 16
f(x) = 0
x^3 + ax^2 + bx + 16 =0 [ f(x) = f(2) = 0]
2^3 + a2^2 + b2 + 16 = 0
8 + 4a + 2b + 16 = 0
2*( 4 + 2a + b+ 8 ) = 0
2a + b + 12 = 0
2a + b = -12 .....(1)
Given ,
a - b = 6.......(2) _______ [ * by 2]
2a - 2b = 12......(3)
subtract eq. (1) from (3) we get....
2a - 2b = 12
-2a + b = -12
----------------------
-3b = 24
b = 24/-3
••••b = -8••••
now putting the value of b in eq. (2) we get
a -( -8) = 6
a = 6 -8
••••a = -2••••