Question

find a quadratic polynomial
sumof whose zeroes is 7
and one of it's zero is 5

be fast guys and no spam ​

Answer 1

$\huge \red{ \boxed{ \bf{ \ulcorner{ \mid{ \overline{ \underline{ANSWER}}}}}\mid }}$

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

→ 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

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

Hence the product of polynomial

$\begin{lgathered}\sf \implies \: \alpha \times \beta \\ \\ \sf \implies \: 5 \times 2 = 10.\end{lgathered}$

NOW THE POLYNOMIAL

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

$\bf \implies \: {x}^{2}$

Answer 2

Hey there

refer to attachment