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TS EAMCET · Maths · Quadratic Equation

If \(-1+i\) is a root of the equation \(x^4+4 x^3+5 x^2+2 x-2=0\), then the real roots of this equation are

  1. A \(-1 \pm \sqrt{3}\)
  2. B \(-1 \pm \sqrt{2}\)
  3. C \(\sqrt{2} \pm 3\)
  4. D \(\sqrt{3} \pm \sqrt{2}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(-1 \pm \sqrt{2}\)

Step-by-step Solution

Detailed explanation

Given, one root is \((-1+i)\). \(\therefore\) Another root will be \((-1-i)\). \((x+1-i)(x+1+i)=x^2+2 x+2\) will be one factor of \(x^4+4 x^3+5 x^2+2 x-2=0\) and thus, \(\frac{x^4+4 x^3+5 x^2+2 x-2}{x^2+2 x+2}, x^2+2 x-1\) will be another factor. \(\therefore\) The roots of…