If P is a second degree polynomial such that P(2) = 5, P?(2) = 3, P?\'(2) = 7;?n
ID: 3286019 • Letter: I
Question
If P is a second degree polynomial such that P(2) = 5, P?(2) = 3, P?'(2) = 7;?nd the value of P(1).Explanation / Answer
Let the polynomial be f(x)=ax^2+bx+c=0............................................................................................................................... Then f(2) -> 4a +2b+c = 5........................................................................................................................................................ f'(2) -> 2ax + b = 4a+b = 3........................................................................................................................................................ f"(2) ->2a = 7 so a = 3.5........................................................................................................................................................... f'(2) = 2(3.5)(2) + b = 3 so b= -11........................................................................................................................................... f(2) = 4(3.5) +2(-11) +c =1, so c = 9...................................................................................................................................... So f(x) = 3.5x^2 -11x +9.......................................................................................................................................................... So f(1) = 3.5(1^2) - 11(1) +9 = 0 so f(1) = 3/2=1.5......................................