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

The Correct Option is B

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:

\( \frac{-7}{2}\)