Question

If P(X)=4x-4 , Find the numbers P(1) and P(2)? b)Write a first degree polynomial q(x) where q(1)=1 and q(2)=5?​

Answer 1

SOLUTION

TO DETERMINE

a. P(x) = 4x - 4, find the numbers P(1) and P(2)

b. Write a first degree polynomial q(x) where q(1) = 1 and q(2) = 5

EVALUATION

a. Here the given polynomial is

P(x) = 4x - 4

Putting x = 1 we get

P(1) = ( 4 × 1 ) - 4 = 4 - 4 = 0

Putting x = 2 we get

P(2) = ( 4 × 2 ) - 4 = 8 - 4 = 4

b. q(x) is a first degree polynomial

Let q(x) = ax + b

q(1) = a + b

q(2) = 2a + b

So by the given condition

a + b = 1 - - - - - (1)

2a + b = 5 - - - - - (2)

Equation 2 - Equation 1 gives

a = 4

From Equation 1 we get

b = 1 - a = 1 - 4 = - 3

∴ q(x) = 4x - 3

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