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JEE Main202228 Jul 2022Morning ShiftMathematicsQuadratic EquationActual

The sum of all real values of x for which 3 x 2 - 9 x + 17 x 2 + 3 x + 10 = 5 x 2 - 7 x + 19 3 x 2 + 5 x + 12 is equal to

Correct answer

0

Step-by-step solution

Given, 3 x 2 - 9 x + 17 x 2 + 3 x + 10 = 5 x 2 - 7 x + 19 3 x 2 + 5 x + 12 ⇒ x 2 + 3 x + 10 + 2 x 2 - 12 x + 7 x 2 + 3 x + 10 = 3 x 2 + 5 x + 12 + 2 x 2 - 12 x + 7 3 x 2 + 5 x + 12 ⇒ 1 + 2 x 2 - 12 x + 7 x 2 + 3 x + 10 = 1 + 2 x 2 - 12 x + 7 3 x 2 + 5 x + 12 ⇒ 2 x 2 - 12 x + 7 1 x 2 + 3 x + 10 - 1 3 x 2 + 5 x + 12 = 0 2 x 2 - 12 x + 7 = 0 Or 3 x 2 + 5 x + 12 = x 2 + 3 x + 10 For 2 x 2 - 12 x + 7 = 0 Sum of roots = 12 2 = 6 Or 3 x 2 + 5 x + 12 = x 2 + 3 x + 10 ⇒   2 x 2 + 2 x + 2 = 0 &#8

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