use the intermediate value theorem to show that the equ p(x) = 3x^3 - 5x^2 - 2x + 5; -1 and 0 p(-1) = p(0) =…

use the intermediate value theorem to show that the equ p(x) = 3x^3 - 5x^2 - 2x + 5; -1 and 0 p(-1) = p(0) = because the signs of the results are opposite need help? read it

use the intermediate value theorem to show that the equ p(x) = 3x^3 - 5x^2 - 2x + 5; -1 and 0 p(-1) = p(0) = because the signs of the results are opposite need help? read it

Answer

Explanation:

Step1: Calculate P(-1)

Substitute x = - 1 into P(x): [ \begin{align*} P(-1)&=3(-1)^{3}-5(-1)^{2}-2(-1)+5\ &=3\times(-1)-5\times1 + 2 + 5\ &=-3-5 + 2+5\ &=-1 \end{align*} ]

Step2: Calculate P(0)

Substitute x = 0 into P(x): [ \begin{align*} P(0)&=3(0)^{3}-5(0)^{2}-2(0)+5\ &=0 - 0-0 + 5\ &=5 \end{align*} ]

Answer:

P(-1)= - 1, P(0)=5