JEE Main202623 January 2026Evening ShiftMathematicsQuadratic EquationActual

The sum of all the real solutions of the equation _ (x+3) (6 x²+28 x+30 )=5-2 _ (6 x+10) (x²+6 x+9 ) is equal to

Options

Correct answer

C. 0

Step-by-step solution

Note 6x^2+28x+30 = 2(3x+5)(x+3) , x^2+6x+9 = (x+3)^2 , 6x+10 = 2(3x+5) . Let a = _ (x+3) [2(3x+5)] . Then LHS = a + 1 and _ 2(3x+5) (x+3)^2 = 2 a . Equation becomes a + 1 = 5 - 4 a , i.e., a^2 - 4a + 4 = 0 a = 2 . So _ (x+3) [2(3x+5)] = 2 (x+3)^2 = 6x+10 x^2 = 1 x = 1 or x = -1 . Both satisfy domain conditions (bases > 0 , 1 ; arguments > 0 ). Sum = 1 + (-1) = 0 .

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 JEE Main PYQs