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: Use the formula for product of zeroes of a quadratic polynomial
For a quadratic polynomial \( ax^2 + bx + c \), the product of zeroes is given by:
\[ \text{Product of zeroes} = \frac{c}{a} \]

Step 2: Identify coefficients from the given polynomial
Given polynomial: \( kx^2 - 4x - 7 \)
Here, \( a = k \), \( b = -4 \), \( c = -7 \)

Step 3: Apply the product of zeroes condition
Given: Product of zeroes = 2
\[ \frac{-7}{k} = 2 \Rightarrow -7 = 2k \Rightarrow k = \frac{-7}{2} \]

Final Answer:
\[ k = \frac{-7}{2} \]