Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main20249 Apr 2024Morning ShiftMathematicsQuadratic EquationActual

Let , be the roots of the equation x^2+2 2 x-1=0 . The quadratic equation, whose roots are ^4+ ^4 and 1 10 ( ^6+ ^6 ) , is :

Options

  1. Ax^2-190 x+9466=0
  2. Bx^2-180 x+9506=0
  3. Cx^2-195 x+9506=0
  4. Dx^2-195 x+9466=0

Correct answer

C. x^2-195 x+9506=0

Step-by-step solution

aligned & x^2+2 2 x-1=0 & + =-2 2 & =-1 & ^4+ ^4= ( ^2+ ^2 )^2-2 ^2 ^2 & = (( + )^2-2 )^2-2( )^2 & =(8+2)^2-2(-1)^2 & =100-2=98 & ^6+ ^6= ( ^3+ ^3 )^2-2 ^3 ^3 & = (( + ) (( + )^2-3 )^2-2( )^3 . aligned aligned & =(-2 2 (8+3))^2+2 & =(8)(121)+2=970 & 1 10 ( ^6+ ^6 )=97 & x^2-(98+97) x+(98)(97)=0 & x^2-195 x+9506=0 aligned

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