Question

The expression x + bx + c leaves the remainder 1 when it is divided by (x + 1) and when it is divided by (x - 2), the remainder is 13. Find the values of b and c. answer b=c=3​

Answer 1

Answer:

Given: p(x)=ax

2

+bx+c, p(0)=−2, p(1)=3 and p(−1)=−3

To find: a,b,c=?

Solution:

p(0)=a(0)

2

+b×0+c

−2=c

c=−2

p(1)=a(1)

2

+b×1−2

3=a+b−2

a+b=5 −−−−−−−−−−−−(1)

p(−1)=a(−1)

2

+b×(−1)−2

−3=a−b−2

a−b=−1 −−−−−−−−−−−−(2)

On adding eqn.(1) and (2) we get,

2a=4

a=2

Put value of a=2 in eqn.(1) we get

2+b=5

b=3

Value of a=2, b=3 and c=−2

p(x)=2x

2

+3x−2

Answer 2

Using remainder theorem here is the answer.