Question

Which of the following quadratic polynomials has zeroes 4 and -2?

• A. \( x^2 - 2x - 8 \)
• B. \( x^2 + 2x - 8 \)
• C. \( x^2 - 2x + 8 \)
• D. \( x^2 + 2x + 8 \)

Hint:

To form a quadratic polynomial from its zeroes, use the formula: \[ x^2 - (\text{sum of zeroes})x + (\text{product of zeroes}) \]

Answer 1

The Correct Option is A

Step 1: The sum of the zeroes is \( 4 + (-2) = 2 \), and the product of the zeroes is \( 4 \times (-2) = -8 \). Step 2: The polynomial whose zeroes are 4 and -2 is given by: \[ x^2 - (\text{sum of zeroes})x + \text{product of zeroes} = x^2 - 2x - 8 \] Thus, the correct answer is \( x^2 - 2x - 8 \).