Find the zeros of the following quadratic polynomial: $p(x) = 3x^2 + 15x$. (in $, -5$)

Obtain a quadratic polynomial with the following conditions:
The sum of the zeros $= -\frac{1}{4}$;
The product of the zeros $= \frac{1}{4}$.

Are the following statements 'True' or 'False'? Justify your answers.
If all three zeroes of a cubic polynomial $x^{3}+ax^{2}-bx+c$ are positive,then at least one of $a, b$ and $c$ is non-negative.

The graph of $p(x) = x^{2} + 6x + 9$ intersects the $X$-axis $\ldots \ldots \ldots \ldots$

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial: $4x^{2} + 5\sqrt{2}x - 3$

Draw the graph of $p(x) = x^3 - 2x^2$ and find the zeros of this polynomial.