Determine what descartes rule of signs says about the number of positive and negative real roots for the polynomial function.

P (x) = x^2+5x+6

see explanation

Step-by-step explanation:

given P (x) = x² + 5x + 6

check the number of sign changes for positive real roots

+ / + / + ← no sign changes ⇒ no positive roots

check the sign changes for P ( - x)

P ( - x) = ( - x) ² + 5 ( - x) + 6 = x² - 5x + 6

+ / - / + ← 2 sign changes ⇒ 2 or 0 negative roots

We can check this by finding the roots

x² - 5x + 6 = 0

(x + 2) (x + 3) = 0 ⇒ x = - 2 or x = - 3 ← 2 negative roots