Question

for what value of k, -2 is a root of 3x^2 +4x +2k= 0

Answer 1

Answer:

$3 {x}^{2} + 4x + 2k = 0 \: \: \: \: \: \: \: \: (let \: x = - 2)$

$3 {( - 2)}^{2} + 4( - 2) + 2k = 0$

$3(4) - 8 + 2k = 0$

$12 - 8 + 2k = 0$

$4 + 2k = 0$

$2k = - 4$

$k = \frac{ - 4}{2}$

$k = - 2$

$\red{For \: k = - 2,\: - 2 \: is \: a \: root \: of \: equation}$

$\red{ \: 3 {x}^{2} + 4x + 2k = 0.}$

Answer 2

Answer:

The value of k is -2.

Given:

• -2 is a root of equation 3x² + 4x + 2k = 0

To find:

• The value of k.

Solution:

The given equation is 3x² + 4x + 2k = 0

Substitute x = -2, we get

=> 3(-2)² + 4(-2) + 2k = 0

=> 3(4) - 8 + 2k = 0

=> 12 - 8 + 2k = 0

=> 4 + 2k = 0

=> 2k = -4

=> k = -2

The value of k is -2.

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Verification:

=> 3x² + 4x + 2(-2) = 0

=> 3x² + 4x - 4 = 0

=> 3x² + 6x - 2x - 4 = 0

=> 3x (x + 2) - 2 (x + 2) = 0

=> (3x - 2) (x + 2) = 0

=> x = 2/3 or -2

The factor of 3x² + 4x + 2k is -2.

Hence, verified.