Question

Find a quadratic polynomial, the
sum of whose zeroes is 7 and one
of the zero is 5.​

Answer 1

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$\huge \pink{ \mid{ \overline{ \underline{ \mathbb{GI} \mathit{V}\mathfrak{EN}}}} \mid}$

→ A polynomial sum of whose zeroes is 7

$\sf{let \: the \: zeroes \: be \: \alpha \: and \: \beta }$

HENCE

$\bf{ \alpha + \beta = 7. }$

♦ It is also given that one of its zero is 5

$\bf{ let \: \alpha = 5.}$

Hence

$\bf{ \alpha + \beta = 7.} \\ \\ \sf{put \: the \: value \: of \: \alpha } \\ \\ \sf \implies \: 5 + \beta = 7. \\ \\ \sf \implies \beta = 7 - 5 \\ \\ \bf \implies \: \beta = 2.$

Hence the product of polynomial

$\sf \implies \: \alpha \times \beta \\ \\ \sf \implies \: 5 \times 2 = 10.$

NOW THE POLYNOMIAL

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

$\bf \implies \: {x}^{2} - 7x + 10.$

Answer 2

Answer:

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