Question

If the sum of the zeros of quadratic polynomial x square + 2 x + 3 k is equal to their product find the value of k

Answer 1

Answer: $-\frac{2}{3}$


The polynomial here is:
$x^2+2x+3k$

Here,

Coefficient of $x^2$ = 1
Coefficient of $x$ = 2
Constant Term = 3k

Now,

$\text{Sum of Zeros }=-\frac{\text{Coefficient of x}}{\text{Coefficient of }x^2}=-\frac{2}{1} = -2 \\ \\ \\ \text{Product of Zeros }=\frac{\text{Constant Term}}{\text{Coefficient of }x^2} = \frac{3k}{1} = 3k$

Now, we are given that:

$\text{Sum of Zeros = Product of Zeros} \\ \\ \\ \implies -2 = 3k \\ \\ \\ \implies \frac{-2}{3} = k \\ \\ \\ \implies \boxed{k = -\frac{2}{3}}$

Thus, the value of k is $-\frac{2}{3}$