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A quadratic function f(x) attains a maximum of $3$ at $x=1.$ The value of the function at $x=0$ is $1.$ What is the value of $f(x)$ at $x=10?$

  1. $-119$
  2. $-159$
  3. $-110$
  4. $-180$
  5. $-105$
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let quadratic equastion f(x) = ax^2+bx+c,

given f(1) = 3, f(0)= 1

at x=0 f(0)=1 so a.0+b.0+c=1 so c=1

x=1 f(1)= 3 so a+b+c= 3

                        a+b=2.... (1)

now f(10)= 100a+10b+1 ....(2)

And here given .. at x=1 f(x) is maximum so df(x)/dx=0

 which is 2ax+b= 0 ,

puting x=1 2a=-b----(3)

    using 1 and 3 a=-2, b=4

now using (2) we get f(10)= -159

so answer is (2)
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