Question

Hi. I need help with these questions.
See image for question.

Answer 1

• a = 3, b = 2

Explanation:

Given

• P(x) = ax² + bx + 1
• P(1) = 6 and P(-1) = 2

To find

• Values of a and b

Solution

Substitute the values of x:

P(1) = 6

• 6 = a(1)² + b(1) + 1
• 6 = a + b + 1
• a + b = 5

P(-1) = 2

• 2 = a(-1)² + b(-1) + 1
• 2 = a - b + 1
• a - b = 1
• a = b + 1

Substitute a in the previous equation:

• a + b = 5
• b + 1 + b = 5
• 2b = 4
• b = 2

Then finding a:

• a = b + 1
• a = 2 + 1
• a = 3

So a = 3, b = 2