The quadratic polynomial `p(x)` ha following properties `p(x)` can be positive or zero for all real numbers `p(1)=0a n dp(2)=2.` Then find the quadratic polynomial.

Answer

`2( x - 1)^(2)`

Explanation

`p(x) `is positive or zero for all real number.
Also p(1) = 0
Then we have` p(x) = k(x - 1)^(2)`, where `l gt 0`
Now p(2) = 2
`rArr k = 2`
`therefore p(x) = 2(x - 1)^(2)`