#### Question

If the sum and product of the roots of the equation kx^{2} + 6x + 4k = 0 are real, then k =

\[- \frac{3}{2}\]

\[\frac{3}{2}\]

\[\frac{2}{3}\]

\[- \frac{2}{3}\]

#### Solution

The given quadric equation is kx^{2} + 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`.

Is there an error in this question or solution?

#### APPEARS IN

Solution If the Sum and Product of the Roots of the Equation Kx2 + 6x + 4k = 0 Are Real, Then K = Concept: Solutions of Quadratic Equations by Factorization.