Chemistry Examples

$7 j + 3 - 4 j + 9$

Step 1

Simplify and reorder the polynomial in descending order to use Descartes rule.

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Step 1.1

Subtract $4 j$ from $7 j$ .

$3 j + 3 + 9$

Step 1.2

Add $3$ and $9$ .

$3 j + 12$

Step 2

To find the possible number of positive roots, look at the signs on the coefficients and count the number of times the signs on the coefficients change from positive to negative or negative to positive.

$f (j) = 3 j + 12$

Step 3

Since there are $0$ sign changes from the highest order term to the lowest, there are at most $0$ positive roots (Descartes' Rule of Signs).

Positive Roots: $0$

Step 4

To find the possible number of negative roots, replace $j$ with $- j$ and repeat the sign comparison.

$f (- j) = 3 (- j) + 12$

Step 5

Multiply $- 1$ by $3$ .

$f (- j) = - 3 j + 12$

Step 6

Since there is $1$ sign change from the highest order term to the lowest, there is at most $1$ negative root (Descartes' Rule of Signs).

Negative Roots: $1$

Step 7

The possible number of positive roots is $0$ , and the possible number of negative roots is $1$ .

Positive Roots: $0$

Negative Roots: $1$