ISRO2009-48

Question

The cubic polynomial $y(x)$ which takes the following values: $y(0)=1, y(1)=0, y(2)=1$ and $y(3)=10$ is

• A. $x^3 +2x^2 +1$
• B. $x^3 +3x^2 -1$
• C. $x^3 +1$
• D. $x^3 -2x^2 +1$

Answer 1

Ans D)

y(x)=x³-2x²+1

Now, putting x=0 we get y(x)=0-0+1=1

Similarly x=1 we get y(x)=0

x=2 then y=1

x=3 then y=10

Answer 2

Answer is D

Option D: x^3 - 2 x^2 +1
=x^2(x-2) +1

Now put x values
you'll get answer as option D

(PS: key point here is solve these type of questions using this technique, take common power of x and then solve)