JEE Main202523 Jan 2025Morning ShiftMathematicsQuadratic EquationActual

If the equation a ( b - c ) x ^2+ b ( c - a ) x + c ( a - b )=0 has equal roots, where a + c =15 and b = 36 5 , then a^2+c^2 is equal to

Correct answer

Step-by-step solution

aligned & a(b-c) x^2+b(c-a) x+c(a-b)=0 & x=1 is root other root is 1 & + =- b(c-a) a(b-c) =2 & - bc + ab =2 ab -2 ac & 2 ac = ab + bc & 2 ac = b ( a + c ) & 2 ac =15 ~b (1) & 2 ac =15 ( 36 5 )=108 & ac =54 & a + c =15 & a ^2+ c ^2+2 ac =225 & a ^2+ c ^2=225-108=117 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 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