Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 201910 AprilEvening Shift
Exam
JEE Main
Year
2019
Date
10 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2019 · 10 April · Evening Shift · Mathematics · Quadratic Equation

The number of real roots of the equation 5 + | 2 ^ x - 1| = 2 ^ x (...

The number of real roots of the equation 5+5 +\left|{2}^{x} - 1\right| = {2}^{x}(2x−2)\left({2}^{x} - 2\right) is :The number of real roots of the equation 5 + | 2 ^ x - 1| = 2 ^ x ( 2 ^ x - 2) is :

Options

  1. A22
  2. B33
  3. C11
  4. D44

Correct answer

C. 11

Step-by-step solution

Let 2x=t{2}^{x} = t

5+∣t−1∣=t2−2t5 + \left|t - 1\right| = {t}^{2} - 2t

⇒∣t−1∣g(t)=(t2−2t−5)f(t)⇒ \mathop{\left|t - 1\right|}_{g\left(t\right)} = \mathop{\left({t}^{2} - 2t - 5\right)}_{f\left(t\right)}

Since, 2x>0∀x∈R⇒t>0{2}^{x} > 0 \forall x \in R ⇒ t > 0

From the graph, we have

The number of real roots of the equation 5 + | 2 ^ x - 1| = 2 ^ x ( 2 ^ x - 2) is :

It is clear from the graph that the two graphs have only one point of intersection.

So, number of real roots of the given equation is 1.1 .

Practice Quadratic Equation on Quantrex Academy →

More from Quadratic Equation

Match each entry in List-I to the correct entry in List-II and choose the correct option.… JEE Advanced 2026Let a, b, c be positive integers in arithmetic progression such that the equation ax^2 +… JEE Advanced 2026Consider the quadratic equation (n^2 - 2n + 2)x^2 - 3x + (n^2 - 2n + 2)^2 = 0 , n ∈ ℝ .… JEE Main 2026Let one root of the quadratic equation in x : (k^2 - 15k + 27)x^2 + 9(k-1)x + 18 = 0 be… JEE Main 2026Let e_1 and e_2 be two distinct roots of the equation x^2 - ax + 2 = 0 . Let the sets \ a… JEE Main 2026Let α, β be the roots of the equation x^2 - x + p = 0 and γ, δ be the roots the equation… JEE Main 2026Let a, b ∈ ℂ . Let α, β be the roots of the equation x^2 + ax + b = 0 . If β - α = 11 and… JEE Main 2026Let A, B , where A, B ∈ (-(π)/(2), (π)/(2)) , be the roots of the quadratic equation x^2… JEE Main 2026If α=1 and β=1+i 2 , where i= -1 are two roots of the equation x^3+ax^2+bx+c=0 , a,b,c ∈… JEE Main 2026If the quadratic equation (λ+2)x^2-3λ x+4λ=0 , λ ≠ -2 , has two positive roots, then the… JEE Main 2026Let α, β be the roots of the equation x^2 - 3x + r = 0 , and (α)/(2), 2β be the roots of… JEE Main 2026Let a, b, c ∈ \ 1, 2, 3, 4\ . If the probability, that ax^2 + 2 2 \,bx + c > 0 for all x… JEE Main 2026Let S=\ x^ 3 +a x^ 2 +b x+c: a, b, c ∈ ~N. and .a, b, c ≤ 20\ be a set of polynomials.… JEE Main 2026If α, β , where α<β , are the roots of the equation λ x^ 2 -(λ+3) x+3=0 such that… JEE Main 2026The smallest positive integral value of a , for which all the roots of x^ 4 -a x^ 2 +9=0… JEE Main 2026The sum of all the real solutions of the equation _ (x+3) (6 x^ 2 +28 x+30)=5-2 _ (6… JEE Main 2026 Full Quadratic Equation list Quadratic Equation JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs