Question

7.Form a quaratic equation From the root 3 and -7

(2 Points)​

Answer 1

Answer: x²+4x-21

Given:

$\sf Roots\:of\:the\:quadratic\:equation\:3\:and\:-7$

To find:

$\sf The\:quadratic\:equation.$

Explanation:

$\sf Let,$

$\sf \:First\:root=\alpha$

$\sf \:Second\:root=\beta$

$\sf Therefore,$

$\sf Sum\:of\:roots=\alpha+ \beta=3+(-7)=-4$

$\sf Product\:of\:roots=\alpha \beta =3\times(-7)=-21$

$\sf We\:know\:that,$

$\boxed{\textbf{ \sf x^2-(\alpha +\beta )x+(\alpha \beta ) }}$

$\sf Substituting\:the\:values\:of\:\alpha\:and\:\beta\:in\:the\:above\:formula,\:we\:get:$

$\sf x^2-(-4 )x+(-21)$

$\boxed{\sf x^2+4x-21}$

Hence, the required equation is x²+4x-21.