For each of the following polynomial, find a quadratic polynomial whose sum and product respectively of the zeros are given. Also obtain the zeros of these polynomial by factorisation.
i)
Polynomial \(=\)
Zeros of the polynomial \(=\)
ii)
Polynomial \(=\)
Zeros of the polynomial \(=\)
Answer variants:
\(16x^{2}-42x+5\)
\(x=\frac{-\sqrt{5}}{2}\) or \(x=\frac{1}{\sqrt{5}}\)
\(2\sqrt{5}x^{2}+3x-\sqrt{5}\)
\(x=\frac{1}{8}\) or \(x=\frac{5}{2}\)