Question

If one root the equation 2x² + kx + 4 = 0 is 2, then the other root is

Options

• 6

• -6

• -1

• 1

Answer 1

Let `alpha and beta `be the roots of quadratic equation`2x^2 + kx + 4 = 0` in such a way that `alpha = 2`

Here, a  = 2, b = k and , c = 4

Then , according to question sum of the roots

`alpha + beta = (-b)/a`

`2+ beta = (-k)/2`

`beta = (-k)/2 - 2`

`beta = (-k -4)/2`

And the product of the roots

`alpha .beta = c /a`

       `= 4/2`

       `= 2`

Putting the value of `beta = (-k -4)/2`in above

`2 xx (-k - 4)/ 2 = 2`

     `(-k - 4) = 2`

                     ` k = -4 -2`

                       `= -6`

Putting the value of k in `beta = (-k - 4)/2`

`beta = (-(6) - 4)/2`

  `= (6-4)/2`

 ` = 2/2`

`beta = 1`

Therefore, value of other root be `beta = 1`