Question

If the sum of zeros of a quadratic polynomial is 3 and their product is -2 then that quadratic polynomial is

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

Hint:

This is a direct application of the formula. Memorize the form \(x^2 - (\text{Sum})x + (\text{Product})\). Be careful with the signs during substitution.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
We are given the sum and product of the zeroes of a quadratic polynomial and need to find the polynomial itself.

Step 2: Key Formula or Approach:
The general form of a quadratic polynomial with a given sum and product of zeroes is:
\[ P(x) = k(x^2 - (\text{sum of zeroes})x + (\text{product of zeroes})) \] We can assume the constant \(k=1\) for simplicity, as it is standard for such problems.

Step 3: Detailed Explanation:
We are given:
Sum of zeroes = 3
Product of zeroes = -2
Substitute these values into the formula:
\[ P(x) = x^2 - (3)x + (-2) \] \[ P(x) = x^2 - 3x - 2 \] This expression matches option (A).

Step 4: Final Answer:
The quadratic polynomial is \(x^2 - 3x - 2\).