Question

Find the value of K for wich x=-2 is a root of the quadratic equation
$kx {}^{2} + x - 6 = 0$

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Answer 1

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\dashrightarrow x=-2$

$\dashrightarrow p(x)= kx^2+x-6=0$

$\large\underline\bold{TO\:FIND,}$

$\dashrightarrow Value\:of\:x$

$\large\underline\bold{SOLUTION,}$

$\therefore Putting\:the\:value\:of\:x\:in\:p(x).we\:get,$

$\dashrightarrow kx^2+x-6=0$

$\implies k(-2)^2+(-2)-6=0$

$\implies 4k-2-6=0$

$\implies 4k-2=6$

$\implies 4k=6+2$

$\implies 4k= 8$

$\implies k= \dfrac{8}{4}$

$\implies k= \cancel \dfrac{8}{4}$

$\implies k= 2$

$\large{\boxed{\bf{ \star\:\: k=2\:\: \star}}}$

VERIFICATION,

$\dashrightarrow kx^2+x-6=0$

$\dashrightarrow x=-2 \\ \dashrightarrow k=2$

$\implies (2)(-2)^2+(-2)-6=0$

$\implies 2(4)-2-6=0$

$\implies 8-8=0$

$\implies 0=0$

$\sf\large\therefore L.H.S= R.H.S$

$\large\underline\bold{VALUE\:OF\:k\:IS\:2.}$

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