Question

10.Find a quadratic polynomial whose sum and product of zeroes are 4,1 respectively.​

Answer 1

Answer:

i hope you got what you want

Answer 2

$Let \: \alpha \: and \: \beta \: are \: two$

$zeroes \: of \: a\:quadratic \: polynomial$

$i) Given \: Sum \:of \:the \: polynomial = 4$

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

$ii) Product \: of \:the \:zeroes = 1$

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

$\therefore \: The \: Quadratic \: polynomial$

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

$Where \:k \: is \: a \: Constant$

$= k (x^{2} - 4x + 1 )$

We can put different values of k.

When k = 1 ,

$\red{ The \: Quadratic \: polynomial \: will}$

$\red{ be } \green { \: x^{2} - 4x + 1 }$

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