Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main201910 Apr 2019Evening ShiftMathematicsQuadratic EquationActual

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

Options

  1. A2
  2. B3
  3. C1
  4. D4

Correct answer

C. 1

Step-by-step solution

Let 2 x = t 5 + t - 1 = t 2 - 2 t ⇒ t - 1 g t = t 2 - 2 t - 5 f t Since, 2 x > 0   ∀ x ∈ R ⇒ t > 0 From the graph, we have 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 .

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. List-I List-II (P) If and are the distinct roots of the equation x^2 + x + 1 = 0 , then th 2026Let a, b, c be positive integers in arithmetic progression such that the equation ax^2 + bx + c = 0 has only integer solutions. Then which of the following statements is (are) TRUE 2026Consider the quadratic equation (n^2 - 2n + 2)x^2 - 3x + (n^2 - 2n + 2)^2 = 0 , n R . Let be the minimum value of the product of its roots and be the maximum value of the sum of it 2026Let one root of the quadratic equation in x : (k^2 - 15k + 27)x^2 + 9(k-1)x + 18 = 0 be twice the other. Then the length of the latus rectum of the parabola y^2 = 6kx is equal to: 2026Let e₁ and e₂ be two distinct roots of the equation x^2 - ax + 2 = 0 . Let the sets a R : e₁ and e₂ are the eccentricities of hyperbolas = ( , ) , and a R : e₁ and e₂ are the eccen 2026Let , be the roots of the equation x^2 - x + p = 0 and , be the roots the equation x^2 - 4x + q = 0 ; p, q Z . If , , , are in G.P., then |p + q| equals : 2026Let a, b C . Let , be the roots of the equation x^2 + ax + b = 0 . If - = 11 and ^2 - ^2 = 3i 11 , then ( ^3 - ^3)^2 is equal to: 2026Let A, B , where A, B (- 2 , 2 ) , be the roots of the quadratic equation x^2 - 2x - 5 = 0 . Then 20 ^2 ( A+B 2 ) is equal to: 2026 Full Quadratic Equation list All JEE Main PYQs