Question

If the sum and product of the roots of the equation kx² + 6x + 4k = 0 are real, then k =

Options

• \[- \frac{3}{2}\]

• \[\frac{3}{2}\]

• \[\frac{2}{3}\]

• \[- \frac{2}{3}\]

Answer 1

The given quadric equation is kx² + 6x + 4k = 0, and roots are equal

Then find the value of c.

Let `alpha and beta`be two roots of given equation

And,  a = k,b = 6 and , c = 4k 

Then, as we know that sum of the roots

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

`alpha +beta = (-6)/a`

And the product of the roots

`alpha. beta = c/a`

  `alpha beta = (4k)/k`

        = 4

According to question, sum of the roots = product of the roots

`(-6)/k = 4`

    `4k = -6`

      `k = (-6)/4`

         `= (-3)/2`

Therefore, the value of `c = (-3)/2`.