Question

Find a quadratic polynomial with the given number as the sum and product of its zeroes respectively

4 , 1

Answer 1

HOLA

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$( \: \alpha \: + \: \beta \: ) \: = \: 4 \: \: \: ( \alpha \beta ) \: = \:1 \\ \\ x {}^{2} \: - ( \: \alpha \: + \: \beta \: ) \: x \: + \: ( \alpha \beta ) \\ \\ \\ x {}^{2} - \: 4x \: + \: 1$
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Answer 2

Hey!!☺☺

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$let \: \: \alpha = 4 \\ \\ \beta = 1 \\ \\ sum \: of \: zeroes \: = 4 \\ \\ \alpha + \beta = 4 \\ \\ product \: of \: zeroes \: = 1 \\ \\ \alpha \beta = 1 \\ \\ required \: polynomial \: \\ = x {}^{2} - ( \alpha + \beta )x + \alpha \beta \\ \\ = x { }^{2} - 4x + 1 \\ \\ hope \: it \: helps$

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