Question

Quadratic polynomial when divided by x - 1 and x - 2 leaves no remainder, then f(x) is

Answer 1

Answer:

Correct option is

C

(x+3)

Let the quadratic polynomial be denoted as P(x).

The polynomial when divided by x+2 gives a remainder of 1. So, from remainder theorom, P(−2)=1.

Similarly, the polynomial when divided by x−1 gives a remainder of 4. So, from remainder theorom, P(1)=4.

Now, if P(x) is divided by the product (x+2)(x−1), the remainder can be at most be a linear function.

We can write P(x)=C(x+2)(x−1)+(Ax+B), where A, B, and C are constants.

Use P(1)=4 and P(−2)=1.

We get two equations: A+B=1 and −2A+B=1.

Solving, we get A=1 and B=3. Hence, the remainder is

Ax+B=x+3