olympicskater5952 olympicskater5952

07-12-2018
Mathematics

contestada

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

Respuesta :

jimrgrant1 jimrgrant1

07-12-2018

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

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