Question

tell a second degree polynomial p(x) with p(0)=0 p(1)=2 and p(2)=6

Answer 1

I hope it will help you.

Answer 2

The required equation is p(x) = x² + x

Given:

A second degree polynomial p(x) with p(0) = 0 p(1) = 2 and p(2) = 6  

To find:

Form the second-degree polynomial p(x)

Solution:

Let the second-degree polynomial p(x) = ax² + bx + c  

Given that p(0) = 0

=>   a(0)² + b(0) + c = 0    

=> c = 0 --- (1)

Given p(1) = 2  

=> a(1)² + b(1) + c = 2      

=> a + b + c = 2

=> a + b = 2 ---- (2)          [ ∵ c = 0 ]    

Given p(2) = 6

=> a(2)² + b(2) + c = 6      

=> 4a + 2b + 0 = 6

=> 4a + 2b = 6  

=> 2a + b =  3 ---- (3)      

Subtract (3) - (2)  

=> 2a + b - (a + b) =  3 - 2

=> 2a + b - a - b = 1

=> a = 1

Substitute a = 1 in a + b = 2  

=> 1 + b = 2

=> b = 1

Now substitute a, b, and c in p(x)

=> p(x) = (1)x² + (1)x + 0

=> p(x) = x² + x

Therefore,

The required equation is p(x) = x² + x

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