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Find the number of +ve and -ve roots of x⁵ - x⁴ + x³ + 8x² + 2x- 2 = 0.

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Detailed Solution

Let. f(x) = x⁵ - x⁴ + x³ + 8x² + 2x - 2

.f{x): +-+++-

f(-x):---+--

There are 3 changes in. f(x) and 2 changes in .f(-x), so (x) has 3 +ve root and 2 negative roots. Thus, the number of real roots = 3 + 2 =5

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