Question

write the quadratic polynomial,sum of whose zeros is 4 and their product is 1.

Answer 1

use quadratic formula

Answer 2

$Let \: \alpha \: and \: \beta\: are \: zeroes \\of \: a \: polynomial$

$i ) Sum \: of \:the \: zeroes = 4$

$\implies \alpha + \beta = 4 \: ---(1)$

$ii) Product\: of \:the \: zeroes = 4$

$\implies \alpha \beta = 1\: ---(2)$

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$\blue {Form \: of \:a \: Quadratic \: polynomial }\\\blue {whose\: zeroes \: are \: \alpha \: and \: \beta}$

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

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/* Required polynomial is:*/

$k[ x^{2} - 4x + 1 ]$

$We \:can \: put \: different \: values \: of \:k$

$When \: k = 1 , \\ \pink { The \: Quadratic \: polynomial \: will \: be } \\\green { x^{2} - 4x + 1 }$

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