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AP EAMCET201920 Apr 2019Morning ShiftMathematicsQuadratic EquationActual

The polynomial equation of degree 4 having real coefficients with three of its roots as (2 3 ) and (1+2 i ), is

Options

  1. A(x^4-6 x^3-14 x^2+22 x+5=0 )
  2. B(x^4-6 x^3-19 x+22 x-5=0 )
  3. C(x^4-6 x^3+19 x-22 x+5=0 )
  4. D(x^4-6 x^3+14 x^2-22 x+5=0 )

Correct answer

D. (x^4-6 x^3+14 x^2-22 x+5=0 )

Step-by-step solution

It is given that, the polynomial equation of degree 4 having real coefficients with three of its roots as (2 3 ) and (l+2 i ), so the remaining root is (1-2 i ). Now, the quadratic equation whose roots as (2 3 ) is (x^2-4 x+1=0 , and ) the quadratic equation whose roots as (1 2 i ), is (x^2-2 x+5=0 ) So, the required polynomial equation is ( aligned (x^2-4 x+1 ) (x^2-2 x+5 ) & =0 x^4-6 x^3+14 x^2-22 x+5 & =0 aligned ) Hence, option (4) is correct.

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