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AP EAMCET202119 Aug 2021Evening ShiftMathematicsQuadratic EquationActual

Value of a for which equations x 3 + a x + 1 = 0 and x 4 + a x 2 + 1 = 0 have a common root

Options

  1. A0
  2. B1
  3. C- 2
  4. Dnone of these.

Correct answer

C. - 2

Step-by-step solution

Given equations are x 3 + a x + 1 = 0 ⇒ x 4 + a x 2 + x = 0       … 1 And, x 4 + a x 2 + 1 = 0       … 2 Subtracting equations 1 and 2 , we get x - 1 = 0 ⇒ x = 1 Thus, x = 1 is the common root. Hence, 1 + a + 1 = 0 ⇒ a = - 2

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