Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
99 Percentile Qs Bank for JEE MainMathematicsQuadratic Equation

Let p and q be roots of the equation x 2 - 2 x + A = 0 and let r and s be the roots of the equation x 2 - 18 x + B = 0 . If p < q < r < s are in A P , then A and B are

Options

  1. A- 3 , - 77
  2. B3 , - 77
  3. C- 3 , 77
  4. D3 , 77

Correct answer

C. - 3 , 77

Step-by-step solution

Let the four numbers in A . P . be p = a - 3 d ,   q = a - d ,   r = a + d ,   s = a + 3 d . Now, p and q are the roots of the quadratic equation x 2 - 2 x + A = 0 . Therefore, using the sum and product of roots of a quadratic equation, we get p + q = 2       … i p q = A       … i i And, r , s are the roots of the quadratic equation x 2 - 18 x + B = 0 . Therefore, r + s = 18       … i i i r s = B       … i v By i and

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 99 Percentile Qs Bank for JEE Main PYQs