The sum of the zeros of a quadratic polynomial $p(x) = x^{2} + 3x + 2$ is ...........

Examine the validity of the following statement: $(x+3)$ is a factor of $(x^{2}+10x+21)$.

For the given sum and product of zeroes,find a quadratic polynomial. Also,find the zeroes of this polynomial by factorisation:
Sum of zeroes = $\frac{-3}{2 \sqrt{5}}$,Product of zeroes = $-\frac{1}{2}$

Are the following statements 'True' or 'False'? Justify your answers.
If the graph of a polynomial intersects the $x$-axis at only one point,it cannot be a quadratic polynomial.

The number of real zeros of $y = p(x)$ is $\ldots \ldots \ldots$ in the given figure.

If the sum of the zeros is $-3$ and the product of the zeros is $-4,$ then the quadratic polynomial is $\ldots \ldots \ldots$