Question

5. The expression x²+bx+a has the same remainder when divided by x - b or x - a. Find the values of a in terms of b. ​

Answer 1

Hi,

Explanation:

P(x)=x²+bx+a

Remainder P(x) divided by x-b is P(b)=b²+b²+a=2b²+a

Remainder P(x) divided by x-a is P(a)=a²+ab+a

Remainders are equal:

2b²+a=a²+ab+a

a²+ab-2b²=0

Searching a:

delta=b²-4*(-2b²)*1=9b²=(3b)²
a=(-b+3b)/2=b

or

a=(-b-3b)/2=-2b