Please explain 

Illustration: The quadratic polynomial p(x) has the following properties :
p(x) can be positive or zero for all real numbers 
p(1) = 0 and p(2) = 2
Then find the quadratic polynomial. 

Sol: p(x) is positive or zero for all real numbers.
Also p(1) = 0
Then we have p(x) = k(x-1)2, where k > 0
Now p(2) = 2
∴ p(x) = 2(x-1)2


Dear student
Since it is given that p(x) is positive or zero for all real numbers.Also given that p(1)=01 will satisfy the required polynomial.(x-1) is a factor of required polynomial.Also no other zero of the required polynomial is given so, we assume that the roots of the required polynomail are perfect square.So, p(x)=k(x-1)2 where k is any non-zero positive constantAlso, given that p(2)=2k=2p(x)=2x-12

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there is nothing to be explained in this question its too simple
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