Question

Determine what Descartes’ Rule of Signs says about the number of positive real roots and negative real roots for the polynomial function. P(x)=9x3-4x2+10

Answer 1

Answer:

Descarte's rule says that the polynomial will have the number of zeroes equal to the number of times  the sign off the coefficient changes.

For positive real roots:

$P(x)=9x^3-4x^2+10$

The coefficient of polynomial is:

+9 -4 +10

There is 2 time sign in changing in 1st and 2nd term and then in 2nd and 3rd term.

So,there will be 2 positive  real roots or less but even.

For negative real roots  find P(-x)

$P(-x)=-(9x^3-4x^2+10)$

$P(-x)=-9x^3+4x^2-10$

So, coefficient of above polynomial is:

-9 +4 -10

There is 2 time sign in changing in 1st and 2nd term and then in 2nd and 3rd term.

So,there will be 2 negative real roots or less but even.