The cubic polynomial y(x) which takes the following values: y(0) = 1, y(1) =…
2009
The cubic polynomial y(x) which takes the following values: y(0) = 1, y(1) = 0, y(2) = 1 y(3) = 10 is
- A.
x3 - 2 x2 + 1
- B.
x3 + 3x2 + 1
- C.
x3 + 1
- D.
x3 +2x2 + 1
Attempted by 8 students.
Show answer & explanation
Correct answer: A
To find the correct cubic polynomial, we substitute each x-value from the given points into the options to see which one matches all y-values. For Option A: x3 - 2x2 + 1. When x=0, y = 0 - 0 + 1 = 1 (matches). When x=1, y = 1 - 2 + 1 = 0 (matches). When x=2, y = 8 - 8 + 1 = 1 (matches). When x=3, y = 27 - 18 + 1 = 10 (matches). Since this polynomial satisfies all four conditions, it is the correct answer. Option B fails at x=1 (1+3+1 !=0). Option C fails at x=1 (1+1 = 2 != 0).