NTA Abhyas JEE Main2020MathematicsQuadratic EquationPractice

The smallest possible natural number n , for which the equation x 2 - n x + 2014 = 0 has integral roots, is

Correct answer

Step-by-step solution

In x 2 - n x + 2014 = 0 α + β = n and α β = 2014 Now, α β = 2014 = 1 × 2014 or - 1 × - 2014 = 2 × 1007 or - 2 × - 1007 = 19 × 106 or - 19 × - 106 = 38 × 53 or - 38 × - 53 For least possible value, n = α + β = 38 + 53 = 91

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 2026 Let 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 2026 Consider 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 2026 Let 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: 2026 Let 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 2026 Let , 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 : 2026 Let 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: 2026 Let 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 NTA Abhyas JEE Main PYQs