Calculate a quadratic polynomial for which the sum of the zeros is \(\sqrt{2}\) and product is \(-\frac{3}{2}\). Find the polynomial and its zeros.
 
Answer:
 
The zeroes are
and
.
Answer variants:
\(x = -\frac{3}{\sqrt{2}}\)
\(x = -\frac{1}{\sqrt{2}}\)
\(x = \frac{1}{\sqrt{2}}\)
\(x = \frac{3}{\sqrt{2}}\)