AP EAMCET · Maths · Quadratic Equation
If \(a \pm i b\) and \(b \pm a i\) are the roots of \(x^4-10 x^3+50 x^2-130 x+169=0\), then \(\frac{a}{b}+\frac{b}{a}=\)
- A \(\frac{25}{12}\)
- B \(\frac{5}{2}\)
- C \(\frac{13}{6}\)
- D \(\frac{34}{15}\)
Answer & Solution
Correct Answer
(C) \(\frac{13}{6}\)
Step-by-step Solution
Detailed explanation
\( (a+ib) + (a-ib) + (b+ai) + (b-ai) = 10 \) \( 2a+2b = 10 \Rightarrow a+b = 5 \) \( (a+ib)(a-ib)(b+ai)(b-ai) = 169 \) \( (a^2+b^2)(b^2+a^2) = 169 \Rightarrow (a^2+b^2)^2 = 169 \Rightarrow a^2+b^2 = 13 \) \( (a+b)^2 = a^2+b^2+2ab \)…
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