Question

help please brainliest
if solved fully I'll mark you as brainliest​

Answer 1

Answer:

p(4) = 99

Step-by-step explanation:

Let the zeroes be α,β,∝.

Given p(x) = x³ + x + 1

Then,

α + β + ∝ = 0

αβ + β∝ + ∝α = 1

αβ∝ = -1

Now,

p(x) = x³ + bx² + cx + d

Given,

p(0) = -1 = -d

p(x) = x³ + bx² + cx - 1

Now,

α² + β² + ∝² = -b

α²β² + β²∝² + ∝²α² = c

α²β²∝² = 1

Now,

α + β + ∝ = 0

⇒ α² + β² + ∝² + 2(αβ + β∝ + ∝α ) = 0

⇒ -b + 2(1) = 0

⇒ b = 2

Now,

αβ + β∝ + ∝α = 1

⇒ α²β² + β²∝² + ∝²α² + 2[α²β²∝ + β²∝²α + ∝α²β] = 1

⇒ c + 2αβ∝[α + β + ∝] = 1

⇒ c + 2(-1)[0] = 1

⇒ c = 1

Now,

p(1) = x³ + 2x² + x - 1

Then,

p(4) = 4³ + 2(4)² + 4 - 1

      = 64 + 32 + 4 - 1

    = 99

Hope it helps!