What is the maximum number of negative real roots which can be formed for the following equation
$x^{8} + 9 x^{6} + 18 x^{5} - 9 x^{3} + 4 x^{2} + 2 x + 1 = 0$ ?

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Solution

The correct option is D 4
To find the number of negative real roots, we need to find the number of sign changes in f(-x)

To find f(-x) replace x by –x in the equation

$f (- x) = x^{8} + 9 x^{6} - 18 x^{5} + 9 x^{3} + 4 x^{2} - 2 x + 1$

Number of sign changes = 4
Maximum number of –ve real roots = 4

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