Question

Form a quadratic polynomial, one of whose zero is (2 +√5) and sum of zeros is 4
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Answer 1

Answer:The polynomial is x2 - 4x - 1. Step-by-step explanation: Sum of zeroes is 4.

Answer 2

Answer:

$let \: \alpha \: and \: \beta \: be \: the \: roots \: of \: quad \: eqn. \\ given \\ \alpha + \beta = 4 \\ = > 2 + \sqrt{5} + \beta = 4 \\ = > \beta = 4 - 2 - \sqrt{5} = 2 - \sqrt{5} \\ now \: \\ product \: of \: zeroes \\ \alpha \beta = (2 + \sqrt{5} )(2 - \sqrt{5} ) = - 1 \\ polynomial = {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ = > {x}^{2} - 4x - 1 = 0 \: is \: the \: req \: polynomial.$