MathematicsIf the sum of the zeros of the quadratic polynomial ft=kt2+2t+3k is equal to their product, find the value of k.

If the sum of the zeros of the quadratic polynomial $f (t) = k t^{2} + 2 t + 3 k$ is equal to their product, find the value of k.

Given that, the sum of the zeros of the quadratic polynomial

f (t) = k t^{2} + 2 t + 3 k

is equal to their product.
We have to find the value of k.
We know that, if

α β

are zeros of quadratic polynomial

a t^{2} + bt + c = 0

, then

α + β = - \frac{b}{a}

and

αβ = \frac{c}{a}

.
Here,
a = k,
b = 2,
c = 3k
So,

α + β = - \frac{2}{k}

and

αβ = \frac{3 k}{k}

\Rightarrow αβ = 3

According to the question,

α + β = αβ

\Rightarrow - \frac{2}{k} = 3

\Rightarrow k = - \frac{2}{3}

Hence, the value of k is

- \frac{2}{3} .

Therefore, option 1 is correct.

JEE