Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
$0 \sqrt{5}$


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Answer 1

Step-by-step explanation:

$\alpha + \beta = - b \div a \: and \: \alpha \times \beta = c \div a$

$\alpha + \beta = 0 \: and \: \alpha \times \beta = \sqrt{5}$

${x}^{2} - ( \alpha + \beta )x + ( \alpha \beta )$

${x}^{2} - 0 + \sqrt{5}$

${x}^{2} + \sqrt{5}$