Class JEE Mathematics Practice Q #716
KNOWLEDGE BASED
APPLY
4 Marks 2023 MCQ SINGLE
The number of real solutions of the equation x^2 + 5|x| + 6 = 0 is:
Prev Next
Explanation
Since |x| is always non-negative, x^2 + 5|x| + 6 is the sum of positive terms plus 6, which can never be zero. Thus, no real solution.

AI Tutor Explanation

Powered by Gemini

Step-by-Step Solution

  1. Given the equation: \(x^2 + 5|x| + 6 = 0\)

  2. Let \(y = |x|\). Then the equation becomes: \(y^2 + 5y + 6 = 0\)

  3. Factor the quadratic equation: \((y + 2)(y + 3) = 0\)

  4. Solve for \(y\): \(y = -2\) or \(y = -3\)

  5. Since \(y = |x|\), \(|x|\) cannot be negative. Therefore, there are no real solutions for \(x\).

Correct Answer: 0

|KEY:0|||

AI generated content. Review strictly for academic accuracy.

Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply their understanding of absolute value functions and quadratic equations to solve the given problem. They must manipulate the equation and determine the number of real solutions.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the concept of absolute value and how it affects the solutions of an equation. It also involves understanding the nature of quadratic equations and their roots.
Syllabus Audit: In the context of JEE, this is classified as KNOWLEDGE. The question directly tests the student's knowledge of quadratic equations and absolute value functions, which are standard topics in the syllabus.

More from this Chapter

MCQ_MULTI
Which of the following compounds show Hydrogen bonding?
ASSERTION_REASON
Assertion: The boiling point of water is higher at lower elevations. Reason: Atmospheric pressure increases as elevation decreases.
MCQ_SINGLE
Let A = {1, 2, 3, ...., 100} and R be a relation on A such that R = {(a, b): a = 2b+1}. Let (a1, аг), (аг, аз), (аз, а4),...., (ak, ak+1) be a sequence of k elements of R such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer k, for which such a sequence exists, is equal to :
MCQ_SINGLE
If the complex number z satisfies |z| = 1 and z ≠ -1, then z/(1+z^2) is purely:
MCQ_SINGLE
Let A = {0, 1, 2, 3, 4, 5}. Let R be a relation on A defined by (x, y) ∈ R if and only if max{x,y} ∈ {3, 4}. Then among the statements (S₁): The number of elements in R is 18, and (S2): The relation R is symmetric but neither reflexive nor transitive
View All Questions