Question

For what value of $k$, the product of zeroes of the polynomial $kx^2 - 4x - 7$ is 2?

• A. $-\frac{1}{14}$
• B. $-\frac{7}{2}$
• C. $\frac{7}{2}$
• D. $-\frac{2}{7}$

Answer 1

Answer: (B)

$-\frac{7}{2}$

Answer 2

We know that for a quadratic equation $ax^2 + bx + c$, the product of the zeroes (roots) is given by:

$\text{Product of the zeroes} = \frac{c}{a}$

In our case, the polynomial is $kx^2 - 4x - 7$, where: $a = k$, $b = -4$, $c = -7$.

We are given that the product of the zeroes is 2. Therefore, we can set up the equation:

$\frac{c}{a} = 2$

Substituting the values of $c$ and $a$:

$\frac{-7}{k} = 2$

Now, solve for $k$:

$-7 = 2k \implies k = \frac{-7}{2}$

Thus, the correct answer is:

$\frac{-7}{2}$