Question

Find the number of positive real roots for equation 3 $x^5$ - 4 $x^4$ - 42 $x^3$ + 56 $x^2$ + 27x - 36 = 0. If all the roots of above given equation are real.

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Answer 1

Solution: Let f(x) = 3 $x^5$ - 4 $x^4$ - 42 $x^3$ + 56 $x^2$ + 27x - 36

According to Descartes' rule of signs

Total number of positive real roots = No. of charges in the sign occurs at any particular terms.

f(x) = 3 $x^5$ - 4 $x^4$ - 42 $x^3$ + 56 $x^2$ + 27x - 36

+ - - + + -

Change Change Change

No. of positive real roots = 3.