Question

if x-3 is a factor of x^2+bx+9,then find the valueb of k

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Answer 1

x-3 is a factor of x² + bx + 9

_________ [GIVEN EQUATION]

We have to find the value of b*.

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• x - 3 = 0

=> x = 3

» Put value of x in x² + bx + 9

=> (3)² + b(3) + 9 = 0

=> 9 + 3b + 9 = 0

=> 3b + 18 = 0

=> 3b = - 18

=> b = - 6 _______ [ANSWER]

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Answer 2

$\huge{ANSWER}$

$\rm{x^2+bx+9}$

$\rm{IF\:x-3\:is\:its\:factor\:then\:x=3\:is\:its\;one\:of\:the\:root}$

$\rm{let\:its\:other\:root\;be\:=\alpha}$

$\implies{\rm{\alpha+3=\frac{-b}{1}}}$

$\boxed{AND}$

$\implies{\rm{\alpha\times\:3=\frac{9}{1}}}$

$\implies{\rm{\alpha=3}}$

$\implies{\rm{3+3=-b}}$

$\implies{\rm{6=-b}}$

$\therefore$ $\rm{b=-6}$

$\rm{FOR\:A\:GENERAL\:QUADRATIC\:EQUATION}$

$\rm{SAY\:ax^2+bx+c}$

$\rm{\alpha+\beta=\frac{-b}{a}}$

$\boxed{AND}$

$\rm{\alpha\times\beta=\frac{c}{a}}$

$\red{\mathbb{HAVE\:A\:GREAT\: FUTURE\:AHEAD}}$