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

-2/

really really sorry if i'm

-12 -5(x + 4) = 3x

-12 - 5x - 20 = 3x

-12 - 20 - 5x = 3x

-32 - 5x = 3x

    + 5x   + 5x

-32 = 8x

8         8

- 4= x