Question

If p(x)=x3-x2+x+1, then find the value of p(1)+p(-1)/2

Answer 1

P(x) = x³ - x² + x + 1

P(1) = 1 - 1 + 1 + 1 = 2

P(-1)/2  = {-1³ - (-1)² -1 + 1}/2

P(-1)/2  =  -2/2 = -1

p(1) + p(-1)/2 = 2-1 = 1

p(1) + p(-1)/2 = 1

Answer 2

The value of p(1)+p(-1)/2  is 1.

Given:

p(x) = x³ - x² + x + 1

To Find:

The value of p(1)+p(-1)/2.

Solution:

It is given that p(x) = x³ - x² + x + 1    ------(1)

We are required to find the value of p(1)+p(-1)/2.

So we must find p(1) and p(-1) values.

In order to find the value of p(1)

We have to substitute x = 1 in equation(1) we get

p(1) = 1³ - 1² + 1 + 1

p(1) = 2

In order to find the value of p(-1)

We have to substitute x = -1 in equation(1) we get

p(-1) = (-1³) - (-1²) + (-1) + 1

p(-1) = -1 -1 -1 +1

p(-1) = -2

P(-1)/2  = {-1³ - (-1)² -1 + 1}/2

p(1)+p(-1)/2  -----(2)

Substitute the values of p(1) and p(-1) in equation(2) we get

p(1)+p(-1)/2  = 2 +((-2)/2)

p(1)+p(-1)/2  = 2 - 1

p(1)+p(-1)/2  = 1

Therefore, The value of p(1)+p(-1)/2  is 1.

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