Exams › JEE Main › Maths

Solve the equation x² + 3*|x| + 2 = 0 over the real numbers. What is its solution set?

1. No real solution (empty set)
2. x = -1, -2
3. x = 1, 2
4. x = -1, -2, 1, 2

Correct answer: No real solution (empty set)

Solution

Put t = |x|, t >= 0. Then t² + 3t + 2 = (t+1)(t+2) = 0 gives t = -1 or t = -2, both negative. Since |x| >= 0, neither is attainable. Also for real x, x² >= 0 and 3|x| >= 0, so x² + 3|x| + 2 >= 2 > 0 always. Hence no real solution.

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 →