Question

using descarts rule of sign . find the nature of the roots of the equation x^4+15x^2+7x-11​

Answer 1

Answer:

(–x) = (–x)5 – (–x)4 + 3(–x)3 + 9(–x)2 – (–x) + 5

= –x5 – x4 – 3x3 + 9x2 + x + 5

I look at the signs:

f (–x) = –x5 – x4 – 3x3 + 9x2 + x + 5

...and I count the number of sign changes:

one sign change