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
- A \(-1 \pm \sqrt{3}\)
- B \(-1 \pm \sqrt{2}\)
- C \(\sqrt{2} \pm 3\)
- D \(\sqrt{3} \pm \sqrt{2}\)
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…
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