AP EAMCET2002MathematicsQuadratic Equation

The maximum possible number of real roots of the equation x^ 5 5 -6 x^2-4 x+5=0 is

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Correct answer

B. 3

Step-by-step solution

Let f(x)=x^2-6 x^2-4 x+5 f(-x)=-x^5-6 x^2+4 x+5 Number of changes of sign in f(x) are 2 and number of changes of sign in f(-x) are 1 . By descarte's rule of signs Maximum number of +ve real roots are 2 and - ve real roots are 1. Maximum possible real roots are 3 .

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