Question

If one root of quadratic equation 2x²+ kx − 6 = 0 is 2, find the value of k. Also, find the other root.​

Answer 1

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Answer 2

Answer:

$\fbox {Given}$

2x²+ kx − 6 = 0

$\fbox {To find}$

Value of k and other root.

$\fbox {Solution}$

Since, x = 2 is a root of the equation

$2x {}^{2} + kx - 6 = 0$

Therefore,

$2 \times 2 {}^{2} + 2k - 6 = 0$

$\Longrightarrow8 + 2k - 6 = 0 \\ \\ \Longrightarrow2k + 2 = 0 \\ \\ \Longrightarrow \: k = - 1 \: \: \: \: \: \: \: \: (1)$

On putting k = -1 in the equation 2x^2 + kx - 6 = 0,

we get 2x^2 - x - 6 = 0

$\Longrightarrow$ 2x(x - 2) + 3(x - 2) = 0

$\Longrightarrow$ (x - 2)(2x + 3) = 0

$\Longrightarrow$ x - 2 = 0, 2x + 3 = 0

$\Longrightarrow$ x = 2, - 3/2

Hence, the other root is -3/2

Thus, value of k is -1 and value of other root is -3/2.