AP EAMCET20226 Jul 2022Morning ShiftMathematicsQuadratic EquationActual

The largest interval containing x for which x ¹²- x ^9+ x ^4- x +1>0 is

Options

A0 < x < 1
B-4 < x < 2
C- < x <
D-2¹⁰ < x < 2¹⁰

Correct answer

C. - < x <

Step-by-step solution

We have f(x)=x¹²-x^9+x^4-x+1 where, f ( x )>0 case I:- when x>1 x ¹²+ x ^4+1>0 and -( x 9+ x ) is also positive f ( x )>0 x " 0 Case III :- when 0 0 & now x ^4 0 as x (0,1) & f ( x )>0 aligned from (i), (ii), (iii)

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