Let $f\left(x\right)$ be a polynomial with integer coefficients satisfying $f\left(1\right)=5$ and $f\left(2\right)=7$. The smallest possible positive value of $f\left(12\right)$ is

If $\alpha , \beta$ and $\gamma$ are the zeros of a cubic polynomial $p\left(x\right)=a{x}^3+b{x}^2+cx+d, a\ne 0$ then $\frac{1}{\alpha }+\frac{1}{\beta }+\frac{1}{\gamma }=$ _____.

The sum of the zeroes of the polynomial $p\left(x\right)=5x^2+2x-3$ is

When $p\left(x\right)=40x^2+11x-63$ is divided by $x+2$ then _____ is obtained as remainder.

The zeros of a quadratic polynomial _____ are $4$ and $3$.