Exams › JEE Main › Maths

Let p(x) be a cubic polynomial with leading coefficient 1 satisfying p(1) = 1, p(2) = 4, and p(3) = 9. Which of the following statements is/are correct?

1. p(4) = 22
2. p(6/5) = (6/5)²
3. p(x) = x² holds for exactly two values of x
4. p(x) = 0 has a root in the interval (0, 1)

Correct answer: p(4) = 22

Solution

Setting g(x) = p(x) - x² gives a monic cubic vanishing at x = 1, 2, 3, so g(x) = (x-1)(x-2)(x-3). All statements can be checked from this explicit form.

Related JEE Main Maths questions

• Let A be the set {(n, 2n): n ∈ N} and let B be the set {(2n, 3n): n ∈ N}. What is the intersection A ∩ B?
• Let set A contain 3 elements and set B contain 6 elements. Then the cardinality of their union must satisfy
• Given the sets A = {1, 2, 5} and B = {3, 4, 5, 9}, what is A ∩ B?
• At a conference with 100 attendees, 29 are Indian women and 23 are Indian men. Among the Indian attendees, 4 are doctors, and 24 are either men or doctors. If there are no foreign doctors, how many foreigners and how many women doctors are present at the conference?
• Let X and Y be two non-empty sets, and let A be a non-empty set such that X ∩ A = Y ∩ A = A and X ∪ A = Y ∪ A. Which of the following must be true?
• If A and B are non-empty sets with A containing B, then which of the following is true?

⚔️ Practice JEE Main Maths free + battle 1v1 →