AP EAMCET · Maths · Quadratic Equation
For \(k>0\), if \(\mathrm{k} \sqrt{-1}\) is a root of the equation \(x^4+6 x^3-16 x^2+24 x-80=0\) then \(k^2=\)
- A 2
- B 3
- C 4
- D 6
Answer & Solution
Correct Answer
(C) 4
Step-by-step Solution
Detailed explanation
\((ki)^4 + 6(ki)^3 - 16(ki)^2 + 24(ki) - 80 = 0\) \(k^4 - 6k^3i + 16k^2 + 24ki - 80 = 0\) \((k^4 + 16k^2 - 80) + (-6k^3 + 24k)i = 0\) \(-6k^3 + 24k = 0\) \(6k(-k^2 + 4) = 0\) \(k^2 = 4\)
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