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AP EAMCET202120 Aug 2021Morning ShiftMathematicsQuadratic EquationActual

If f x = 2 x 3 + m x 2 - 13 x + n and 2 , 3 are roots of the equation f x = 0 , then the values of m and n are -

Options

  1. A- 5   ,   - 30
  2. B- 5   ,   30
  3. C5   ,   30
  4. DNone of these

Correct answer

B. - 5   ,   30

Step-by-step solution

f x = 2 x 3 + m x 2 -   13 x + n Since 2   &   3 are roots of equation f x = 0 So f 2 = 0 ⇒ 16 + 4 m - 26 + n = 0 ⇒ 4 m + n - 10 = 0       . . . . i f 3 = 0 ⇒ 54 + 9 m   -   39 + n = 0 ⇒ 9 m + n + 15 = 0         . . . . ii Subtracting equation i and ii , we get 5 m + 25 = 0 ⇒ m = -   5 Put m = - 5 in equation i , we get n = 30

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