Question

if one root of the quadratic equation 2x² + kx - 2 = 0 is –2, find the value of k​

Answer 1

ANSWER✔

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

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

$\dashrightarrow x= -2$

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

$\dashrightarrow The\:value\:of\:k.$

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

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

$\dashrightarrow 2(-2)^2+k(-2)-2=0$

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

$\implies 8-2k-2=0$

$\implies 6-2k=0$

$\implies -2k=-6$

$\implies \cancel{-}\:2k= \cancel{-}\:6$

$\implies 2k=6$

$\implies k= \dfrac{6}{2}$

$\implies k= \cancel \dfrac{6}{2}$

$\implies k= 3$

$\large{\boxed{\bf{ \star\:\:k= 3 \:\: \star}}}$

VERIFICATION,

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

$\dashrightarrow x=-2\\ \dashrightarrow k= 3$

$\implies 2(-2)^2+(3)(-2)-2=0$

$\implies 8-6-2=0$

$\implies 2-2=0$

$\implies 0=0$

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

HENCE VERIFYED✔

$\large\underline\bold{THE\:VALUE\:OF\:k\:IS:3}$

______________

Answer 2

SOLUTION

GIVEN

One root of the quadratic equation 2x² + kx - 2 = 0 is - 2

TO DETERMINE

The value of k

EVALUATION

Here the given Quadratic equation is

2x² + kx - 2 = 0

Now - 2 is a root of the equation

This gives

$\sf{2 \times {( - 2)}^{2} + k \times ( - 2) - 2 = 0 }$

$\sf{ \implies \: 2 \times 4 - 2k - 2 = 0 }$

$\sf{ \implies \:8 - 2k - 2 = 0 }$

$\sf{ \implies \:6 - 2k = 0 }$

$\sf{ \implies \: - 2k = - 6 }$

$\sf{ \implies \: k = 3 }$

FINAL ANSWER

Hence the required value of k = 3

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