Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202622 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
22 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Functions

JEE Main 2026 · 22 January · Morning Shift · Mathematics · Functions

The number of distinct real solutions of the equation...

The number of distinct real solutions of the equation x∣x+4∣+3∣x+2∣+10=0x|x+4|+3|x+2|+10=0 is

Options

  1. A2
  2. B1
  3. C3
  4. D0

Correct answer

B. 1

Step-by-step solution

Equation: x∣x+4∣+3∣x+2∣+10=0x|x+4| + 3|x+2| + 10 = 0.
Critical points: x=−4,−2x = -4, -2.
Case 1:
x≥−2x \ge -2: x(x+4)+3(x+2)+10=0x(x+4) + 3(x+2) + 10 = 0
⇒x2+7x+16=0\Rightarrow x^2+7x+16=0.
Discriminant =49−64=−15<0= 49-64 = -15 < 0. No real roots.

Case 2:
−4≤x<−2-4 \le x < -2: x(x+4)−3(x+2)+10=0x(x+4) - 3(x+2) + 10 = 0
⇒x2+x+4=0\Rightarrow x^2+x+4=0.
Discriminant =1−16=−15<0= 1-16 = -15 < 0. No real roots.

Case 3:
x<−4x < -4: −x(x+4)−3(x+2)+10=0-x(x+4) - 3(x+2) + 10 = 0
⇒x2+7x−4=0\Rightarrow x^2+7x-4=0.
x=−7±652x = \frac{-7 \pm \sqrt{65}}{2}.
x=−7+652≈0.53x = \frac{-7+\sqrt{65}}{2} \approx 0.53 (rejected, not in x<−4x<-4). x=−7−652≈−7.53x = \frac{-7-\sqrt{65}}{2} \approx -7.53 (valid).

Number of distinct real solutions =1= 1.
Practice Functions on Quantrex Academy →

More from Functions

Let ℕ denote the set of all positive integers. Consider the sets A = \ 1, 2, 3, 4, 5\ and… JEE Advanced 2026Let f:(1,∞)→ℝ be a function defined as f(x) = (x-1)/(x+1) . Let f^ i+1 (x) = f(f^i(x))… JEE Main 2026Let f be a polynomial function such that _2(f(x)) = ( _2(2+(2)/(3)+(2)/(9)+…∞))·… JEE Main 2026Let f: ℝ arrow ℝ be defined as f(x) = (2x^2 - 3x + 2)/(3x^2 + x + 3) . Then f is : JEE Main 2026Let e be the base of natural logarithm and let f: \ 1, 2, 3, 4\ arrow \ 1, e, e^2, e^3\… JEE Main 2026Let f: R arrow R be a function such that f(x) + 3f((π)/(2) - x) = x , x ∈ R . Let the… JEE Main 2026The sum of all the integral values of p such that the equation 3 ^2 x + 12 x - 3 = p , x… JEE Main 2026Let A = \ 1, 2, 3, 4, 5, 6\ . The number of one-one functions f: A arrow A such that f(1)… JEE Main 2026For the function f:[1,∞) arrow [1,∞) defined by f(x)=(x-1)^4+1 , among the two… JEE Main 2026Let for some α ∈ ℝ , f:ℝarrowℝ be a function satisfying f(x+y)=f(x)+2y^2+y+α xy for all… JEE Main 2026Let [·] denote the greatest integer function. If the domain of the function f(x) = ^ -1… JEE Main 2026The number of functions f: \ 1, 2, 3, 4\ arrow \ a, b, c\ , which are not onto, is: JEE Main 2026If the domain of the function f(x) = _ (0.6) (|(2x-5)/(x^2-4)|) is (-∞, a] \ b\ [c, d)… JEE Main 2026Given below are two statements: Statement I: The function f: R arrow R defined by… JEE Main 2026The sum of all the elements in the range of f(x)=Sgn( x)+Sgn( x)+Sgn( x)+Sgn( x) , x ≠ n… JEE Main 2026If g(x)=3 x^ 2 +2 x-3, f(0)=-3 and 4 g(f(x))=3 x^ 2 -32 x+72 , then f(g(2)) is equal to: JEE Main 2026 Full Functions list Functions JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs