Question

Which of the following quadratic polynomials has sum of zeroes \(-3\) and product of zeroes \(2\)?

• A. \(x^{2}+3x+2\)
• B. \(x^{2}+2x-3\)
• C. \(x^{2}-3x-2\)
• D. \(x^{2}-3x+2\)

Hint:

Given sum \(S\) and product \(P\), write \(x^{2}-Sx+P\) directly.

Answer 1

The Correct Option is A

Step 1: Build quadratic from sum \(S\) and product \(P\).
A monic quadratic with sum \(S\) and product \(P\) is \(x^{2}-Sx+P\).
Step 2: Substitute \(S=-3,\ P=2\).
\(x^{2}-(-3)x+2 = x^{2}+3x+2\).