The number of positive real roots for polynomial equation f(x) is given by________.
No. of times sign is changing in f(-x)
Total number of positive terms in f(x)
Degree of the equation
No. of times sign is changing in f(x)
The number of positive real roots for polynomial equation f(x) is given by No. of times sign is changing in f(x)
Find the number of complex roots for a 12th degree polynomial f(x) if there is no positive and negative real roots but f(0) = 0.
Let P, Q, R, S and T are five sets about the quadratic equation (a – 5)x2 – 2ax + (a – 4) = 0, a ≠ 5 such that P : All values of ‘a’ for which the product of roots of given quadratic equation is positive. Q : All values of ‘a’ for which the product of roots of given quadratic equation is negative. R : All values of ‘a’ for which the product of real roots of given quadratic equation is positive. S : All values of ‘a’ for which the roots of given quadratic are real. T : All values of ‘a’ for which the given quadratic equation has complex roots.