Question

Form a quadratic polynomial, the sum and
product of whose zeroes are - 7 and 10.​

Answer 1

Answer:

quadratic equation is expressed by

x^2-Sx+P

here S --sum of roots

P=products of roots

the quadratic equation

x^2+7x+10

ok

follow me

gys

Answer 2

Step-by-step explanation:

• Sum of Zeroes ( α + β ) = - 7

• Product of Zeroes ( αβ ) = 10

Quadratic Polynomial = ?

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

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

⠀

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

$\rule{180}{1.5}$

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