Question

 If one root of the quadratic equation 2x² + kx – 6 = 0 is 2, the value of k is___________.​

Answer 1

Answer:

$2 {x}^{2} + kx - 6 = 0 \\ 2( {2}^{2} ) + 2k - 6 = 0 \\ 8 + 2k - 6 = 0 \\ 2 + 2k = 0 \\ 2k = - 2 \\ k = \frac{ - 2}{2} \\ k = - 1$

Answer 2

Solution :

The given quadratic equation is :

> f(x) =2x^2 + kx  - 6 = 0

Let this equation have two roots, α and β.

So,

f(α) = 2α² + kα - 6 = 0

Now, it is mentioned that one of the roots is 2.

So, f(2) = 0

> 2 * 4 + 2k - 6 = 0

> 8 - 6 = 2k

> 2k = 2

> k = -1

The equation thus becomes :

> 2x^2 - x - 6 = 0

Let us find the other root as well by factorization.

2x^2 - 3x + 2x - 6 = 0

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

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

> x = -2 and x = 2/3

Answer : The required value of k is 1.

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