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if f(x)={ax^2+2bx+c]/[Ax^2 +2Bx+C] has extrem points at x=1 and x=-1 such that f(1)=2, f(-1)=3 and f(0)=2.5 then find the value of the function f(x).

if f(x)={ax^2+2bx+c]/[Ax^2 +2Bx+C] has extrem points at x=1 and x=-1 such that f(1)=2, f(-1)=3 and f(0)=2.5 then find the value of the function f(x).

Grade:12

1 Answers

Vikas TU
14149 Points
2 years ago
Dear student 
The question is saying that f(1)=3
It means that on putting x = 1, we get 3 as remainder
f(1)= a(1)^2 + b(1) +2
3 = a+b + 2
a+b = 1 -----------------(1)
Now,
Second case
f(4)=42
a(4)^2 + b(4) + 2 = 42
16a + 4b = 40
4a+b = 10 ------------------(2)
Subtracting equation 1 from 2, we get
3a= 9
a=3
Now,
On putting the value of a in equation 1, we get
b= - 2

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