Question

Which of the following polynomial has roots 4 and -2?

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

Hint:

The quadratic equation for given roots \( \alpha, \beta \) is: \[ (x - \alpha)(x - \beta) = 0. \]

Answer 1

The Correct Option is A

Step 1: The polynomial with given roots \( \alpha \) and \( \beta \) is:
\[ (x - \alpha)(x - \beta) = 0. \] Step 2: Substituting \( \alpha = 4 \), \( \beta = -2 \):
\[ (x - 4)(x + 2) = 0. \] Step 3: Expanding:
\[ x^2 + 2x - 4x - 8 = x^2 - 2x - 8. \]