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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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