Question

The number of positive real roots for any degree of equation f(x) is given by________.

• A. Total number of positive terms in f(x)
• B. Degree of the equation
• C. No. of times sign is changing in f(-x)
• D. No. of times sign is changing in f(x)

Answer 1

The correct option is D

No. of times sign is changing in f(x)

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 times sign is changing in f(x).

For eg.

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

+ + + + + -

Change

No. of positive real roots = 1