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If the sum of the roots of the equation $k x^{2} + 2 x + 3 k = 0$ is equal to their product, then the value of k is

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\frac{1}{3}

- \frac{1}{3}

\frac{2}{3}

- \frac{2}{3}

answer is D.

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Detailed Solution

Given quadratic is,

k x^{2} + 2 x + 3 k = 0

.
Also,
Sum of the roots = Product of the roots
We know that,
The standard form of a quadratic equation is

a x^{2} + bx + c = 0,

where

a, b c

are real numbers and

a \neq 0

.
And, the sum of the roots is given by

- \frac{b}{a}

and product of the roots is given by

\frac{c}{a}

.
After comparing

k x^{2} + 2 x + 3 k = 0

with the standard form, we get,

a = k, b = 2, c = 3 k

.
Then,
Sum of the roots =

- \frac{b}{a} = \frac{2}{k}

.
Product of the roots =

\frac{c}{a} = \frac{3 k}{k} = 3

.
According to the given condition,

⟹ - \frac{2}{k} = 3

⟹ - 2 = 3 k

∴ k = - \frac{2}{3}

∴

If the sum of the roots of the equation

k x^{2} + 2 x + 3 k = 0

is equal to their product, then the value of k is

- \frac{2}{3}

Hence, the correct option is 4.

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