Exams › JEE Advanced › Maths
A cubic polynomial P(x) has leading coefficient 3 and satisfies P(1) = 1, P(2) = 2, P(3) = 3. Find P(4).
- 4
- 22
- 28
- 7
Correct answer: 22
Solution
Let Q(x) = P(x) - x. Since P(1)=1, P(2)=2, P(3)=3, Q has roots 1, 2, 3. P is cubic with leading coefficient 3, and subtracting x (degree 1) does not change the leading term, so Q(x) = 3*(x-1)*(x-2)*(x-3). Then P(x) = 3*(x-1)*(x-2)*(x-3) + x, so P(4) = 3*(3)*(2)*(1) + 4 = 18 + 4 = 22.
Related JEE Advanced Maths questions
- When a polynomial f(x) is divided by x² - 3x + 2, the remainder is a*x + b. Given f(1) = 4 and f(2) = 7, find the values of a and b.
- A polynomial f(x) of degree 4 satisfies f(1) = 1, f(2) = 2, f(3) = 3, f(4) = 4, and f(0) = 1. Find f(5).
- In a chemistry class, there are 20 students, while a physics class has 30 students. If 10 students are enrolled in both classes, and the two classes are held at separate times, determine the value of k/8, where k represents the total number of students attending either class.
- Given that A represents the divisors of 15, B contains prime numbers less than 10, and C includes even numbers less than 9, how many elements are there in the intersection of (A ∪ C) and B?
- Identify the periodic function among the following:
- The function f(x) = √|x² - 5| x + 6 + √8 + 2|x| - |x|² is defined as a real number for values of x within which range?
⚔️ Practice JEE Advanced Maths free + battle 1v1 →