If $a+b+c=9$ and $a b+b c+c a=26,$ find $a^{2}+b^{2}+c^{2}.$

Write whether the following statements are True or False. Justify your answer.

$\frac{1}{\sqrt{5}} x^{\frac{1}{2}}+1$ is a polynomial

Factorise

$x^{3}+12 x^{2}+39 x+28$

The zero of polynomial $5 x-10$ is............

Find the value of each of the following polynomials at the indicated value of variables

$q(y)=5 y^{3}-4 y^{2}+14 y-\sqrt{3}$ at $y=2$

The following expressions are polynomials? Justify your answer:

$\frac{1}{7} a^{3}-\frac{2}{\sqrt{3}} a^{2}+4 a-7$