Question

form a quadratic polynomial the sum and product of whose zeros are - 7 and 10​

Answer 1

X2(square) + (Alfa +beta)*x -(Alfa*beta)...

so according to the question...

Alfa+beta= -7

Alfa*beta= 10..

so...X2(square) +(-7)x -(+10)

so.....X2(square) -7x -10....

so the answer is..x2 - 7x - 10..

Hope this helps you out!!

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Answer 2

Step-by-step explanation:

• Sum of Zeroes ( α + β ) = - 7

• Product of Zeroes ( αβ ) = 10

• Quadratic Polynomial = ?

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf Polynomial=x^2-(Sum\:of\:Zeroes)x+Product\:of\:Zeroes\\\\\\:\implies\sf Polynomial=x^2 -(\alpha + \beta)x + ( \alpha \beta)\\\\\\:\implies\sf Polynomial=x^2 - ( - 7)x + 10\\\\\\:\implies\underline{\boxed{\sf Polynomial=x^2 + 7x + 10}}$

⠀

$\therefore\:\underline{\textsf{Required polynomial is 2) \textbf{x ^\text2 + 7x + 10}}}.$

$\rule{180}{1.5}$

$\boxed{\begin{minipage}{5.5 cm} { \bigstar\: \textsf{For a Quadratic Polynomial :}}\\\\ {\qquad\sf p(x) = ax ^\sf2 \sf + bx + c}\\\sf with zeroes \alpha\:\sf and\:\beta \\\\\\ {\textcircled{\footnotesize1}} \:\:\alpha +\beta= \dfrac{ - \:b}{a}\:\:\bigg\lgroup\bf Sum\:of\:Zeroes\bigg\rgroup \\\\\\{\textcircled{\footnotesize2}} \: \:\alpha \beta= \sf\dfrac{c}{a}\:\:\bigg\lgroup\bf Product\:of\:Zeroes\bigg\rgroup\end{minipage}}$