AP EAMCET · Maths · Quadratic Equation
The largest interval containing \(\mathrm{x}\) for which \(\mathrm{x}^{12}-\mathrm{x}^9+\mathrm{x}^4-\mathrm{x}+1>0\) is
- A \(0 < x < 1\)
- B \(-4 < x < 2\)
- C \(-\infty < \) x \( < \infty\)
- D \(-2^{10} < x < 2^{10}\)
Answer & Solution
Correct Answer
(C) \(-\infty < \) x \( < \infty\)
Step-by-step Solution
Detailed explanation
We have \(f(x)=x^{12}-x^9+x^4-x+1\) where, \(\mathrm{f}(\mathrm{x})>0\) case I:- when \(x>1\) \(\mathrm{x}^{12}+\mathrm{x}^4+1>0\) and \(-(\mathrm{x} 9+\mathrm{x})\) is also positive \[ \Rightarrow \mathrm{f}(\mathrm{x})>0 \quad \forall \mathrm{x} " 0 \] Case III :- when…
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