AP EAMCET · Maths · Complex Number
If \(x\) is complex, the expression \(\frac{x^2+34 x-71}{x^2+2 x-7}\) takes all values which lie in the interval \((a, b)\), find the value of \(a\) and \(b\).
- A \(a=-1, b=1\)
- B \(a=1, b=-1\)
- C \(a=5, b=9\)
- D \(a=9, b=5\)
Answer & Solution
Correct Answer
(C) \(a=5, b=9\)
Step-by-step Solution
Detailed explanation
Here we have to find range of \(\frac{x^2+34 x-71}{x^2+2 x-7}=y\) (Let) Then, \(\begin{gathered} x^2+34 x-71=x^2 y+2 x y-7 y \\ \Rightarrow \quad x^2(y-1)+x(2 y-34)+(71-7 y)=0 \end{gathered}\) As \(x\) is complex, directriminant of above equation,…
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