(i) if both x-2 and x-1/2 are factors of px2 +5x + r , show that p=r
(ii)if the polynomial az3+4z2+3z-4 and z3-4z+a leave the same remainder when divided by z-3 find 'a'
(1) Given polynomial is –
Solving (1) and (2) –
Multiplying (2) by 4, we obtained –
Subtracting (3) from (1), we get –
and so from (1) , we get –
Hence, r = p = –2
(2) Given polynomials are –
Divide p1(x) by z – 3 and get the remainder as follows :
Thus, the remainder is –
Now divide p2(x) by z – 3 and get the remainder as given below –
Here, the remainder is –
According to question –