Question

Find the quadratic polynomial, the sum of whose root is $\sqrt{2}$ and their product is $\frac{1}{3}$

Answer 1

We can find the quadratic equation if we know the sum of the roots and product of the roots by using the formula
x² − (Sum of the roots)x + Product of roots = 0
$$\begin{gathered} \Rightarrow x^2-\sqrt{2}x+\frac{1}{3}=0 \\ \Rightarrow 3x^2-3\sqrt{2}x+1=0 \end{gathered}$$