Mathematics - Application of Derivative Question with Solution | TestHub

One of the roots of the equation $f(x)=0$ is an even prime integer where $f(x)=x^2-ax+b$ ('a' is an odd positive integer). Also known that ${\sum }_{i=1}^{5}f(i)=20$ and two curves are defined as $C_1:y^2=f(x)$ and $C_2:y^2=-f(x)$.

Equation of normals to the curve $y=f(x)$ which are parallel to the tangent from origin to the curve $C_2$ are $\pm \frac{x}{\sqrt{t}}=ty-v$, (where 't' and 'v' are real constants) then 't' equals.