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

Step 1: Recall the formula for the product of zeroes of a quadratic polynomial
For a quadratic polynomial of the form \( ax^2 + bx + c \), the product of its zeroes is calculated as:
\[\text{Product of zeroes} = \frac{c}{a}\]

Step 2: Determine the coefficients of the provided polynomial
The given polynomial is \( kx^2 - 4x - 7 \). From this, we identify the coefficients:
\( a = k \), \( b = -4 \), \( c = -7 \)

Step 3: Utilize the given product of zeroes
It is stated that the product of the zeroes is 2.
Using the formula from Step 1 and the coefficients from Step 2:
\[\frac{-7}{k} = 2\]
Solving for k:
\[-7 = 2k\]
\[k = \frac{-7}{2}\]

Final Answer:
The value of k is:
\[k = \frac{-7}{2}\]