Question

A quadratic polynomial having zeroes 0 and -2, is

• A. \( x(x-2) \)
• B. \( 4x(x+2) \)
• C. \( x^2 + 2 \)
• D. \( 2x^2 + 2x \)

Answer 1

The Correct Option is B

Given:
Zeroes of the quadratic polynomial are \(0\) and \(-2\).

Step 1: Use zeroes to write the polynomial
If zeroes are \(\alpha\) and \(\beta\), polynomial can be written as:
\[ k(x - \alpha)(x - \beta) \] Here, \(\alpha = 0\) and \(\beta = -2\), so:
\[ k(x - 0)(x - (-2)) = kx(x + 2) \]

Step 2: Choose the constant \(k\)
Given the polynomial is \(4x(x + 2)\), so \(k = 4\).

Final Answer:
\[ \boxed{4x(x + 2)} \]