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Find a quadratic polynomial, the sum and product of whose zeroes are \(\frac{-3}{2\sqrt{5}}\) and \(-\frac{1}{2}\), respectively. Also, find its zeroes of the polynomial by factorisation.
Answer:
Quadratic polynomial \(=\)
The zeroes are and .
Answer variants:
\(x = -\frac{1}{\sqrt{5}}\)
\(x = \frac{\sqrt{5}}{2}\)
\(x^2 + \frac{3}{2\sqrt{5}}x - \frac{1}{2}\)
\(x = \frac{1}{\sqrt{5}}\)
\(x^2 - \frac{3}{2\sqrt{5}}x - \frac{1}{2}\)
\(x = \frac{-\sqrt{5}}{2}\)
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