Question

The number of distinct real roots of x^4-4x^3+12x^2+x-1=0

Answer 1

Using Descartes’ Rule of Signs:

3 Sign Changes....So... 3 but the answer shuld be 2....hw?

Answer 2

@satellite73

Answer 3

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Answer 4

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Answer 5

Don't forget the possible negative real roots as well.

Answer 6

- ve roots

f(-x) = x^4-4x^3+12x^2+x-1

+ + + - -

oh....1 - ve root

Answer 7

Descartes' rule of signs tells you the possible numbers of positive real and negative real roots by looking at the sign changes in f(x) and f(-x).
The sign changes in f(x) give possible number of positive real roots.
The sign changes in f(-x) give possible number of negative real roots.

Answer 8

There ya' go.
So there could be 3 or 1 positive real roots, and there is 1 negative real roots.

Answer 9

If there are only 2 real roots then that means that one of them is positive, the other negative, and the other two roots are imaginary.