Answer:
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
