Question

if f(x)=ax^2+bx+2 and f(1)=3, f(4)=42 then find a and b

Answer 1

I've done it ..answer is 3,-2

Answer 2

First case

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

Hope it help you

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