What are the relationship between zeroes and signs of coefficients of Polynomial ?

Find zeros of $p\left(x\right)=x^2+9x+14$. Also find the sum and product of the zeros.

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

Find a quadratic polynomial whose zeros are reciprocals of the zeros of the polynomials $f\left(x\right)=a{x}^2+bx+c, a\ne 0, c\ne 0.$

If $\alpha$ and $\beta$ are the zeroes of polynomial $2x^2-4x+5$, then find the value of $\frac{1}{\alpha }+\frac{1}{\beta }$.

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 $\frac{1}{\alpha }+\frac{1}{\beta }+\frac{1}{\gamma }=$ _____.

If the sum of zeros of the polynomial $a{x}^2-8x-4 is 4,$ then find the value of $a.$

Find the zeroes of the quadratic polynomial $3x^2-x-4$ and verify the relationship between the zeroes and the coefficients.