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AP EAMCET202318 May 2023Evening ShiftMathematicsQuadratic EquationActual

If P ( x )=0 is a polynomial equation of least degree with integer coefficients and 2 + 3 i is one of its roots, then that equation is

Options

  1. Ax ^6-2 x ^4+2 x ^2-25=0
  2. Bx^5+3 x^4+2 x^2+24=0
  3. Cx^4+2 x^2+25=0
  4. Dx^4-2 x^2+25=0

Correct answer

C. x^4+2 x^2+25=0

Step-by-step solution

( 2 + 3 i) is a root of P ( x ) then ( 2 - 3 i ) , (- 2 + 3 i) and (- 2 - 3 i) will also be roots of p(x) aligned & (x-( 2 + 3 i))(x-( 2 - 3 i))(x-(- 2 + 3 i)) & (x-(- 2 - 3 i))=0 & (x^2-2 2 x+5 ) (x^2+2 2 x+5 )=0 & (x^2+5 )^2-(2 2 x)^2=0 & x^4+25+10 x^2-8 x^2=0 & x^4+2 x^2+25=0 aligned

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