The zero of the linear polynomial $p(x) = \sqrt{3}x - 3$ is ............

Find $k$ such that $x^{2}+2x+k$ is a factor of $2x^{4}+x^{3}-14x^{2}+5x+6$. Also,find all the zeroes of the two polynomials.

The maximum number of zeros of $p(x) = ax^4 + bx^3 + cx^2 + dx + e$ where $a \neq 0$ and $a, b, c, d, e \in R$ can be:

The number of polynomials having zeroes as $-2$ and $5$ is

Prove that $-6, -\frac{1}{2}$ and $1$ are the zeros of the cubic polynomial $p(x) = 2x^3 + 11x^2 - 7x - 6$. Also,verify the relationship between the zeros and the coefficients.

What must be added to the polynomial $p(x) = 6x^5 + 5x^4 + 11x^3 - 3x^2 + x + 1$ so that the resulting polynomial is exactly divisible by $3x^2 - 2x + 4$? (Hint: add $-r(x)$ to $p(x)$)