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Multiple choice

Let $f(x)=4x^{2}-4ax+a^{2}-2a+2$ be quadratic polynomial in $x$ and $a$ is any real number if both roots of $f(x)=0$ lie in $(0,2)$ then the value of $a$ belong to

  1. $\left[1,5-\sqrt {7}\right]$
  2. $\left(-\infty,5-\sqrt {7}\right)$
  3. $\left(5+\sqrt {7},\infty\right)$
  4. $\left(1-\infty,\infty\right)$
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