Question

The zeroes of the polynomial \(2x^2 - 4x - 6\) are

• A. 1, 3
• B. -1, 3
• C. 1, -3
• D. -1, -3

Hint:

Always look for a common factor in the polynomial terms before factoring. It simplifies the numbers and makes the factorization process easier.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The zeroes of a polynomial P(x) are the values of x for which P(x) = 0. For a quadratic polynomial, we can find the zeroes by factoring the polynomial, using the quadratic formula, or by splitting the middle term.

Step 2: Key Formula or Approach:
We will find the zeroes by setting the polynomial equal to zero and solving for x. Let's use the factorization method by splitting the middle term.
The polynomial is \(P(x) = 2x^2 - 4x - 6\).
Set \(P(x) = 0\):
\[ 2x^2 - 4x - 6 = 0 \]

Step 3: Detailed Explanation:
First, we can simplify the equation by dividing the entire equation by 2, as it is a common factor.
\[ x^2 - 2x - 3 = 0 \] Now, we need to find two numbers that multiply to -3 and add up to -2. These numbers are -3 and 1.
Split the middle term:
\[ x^2 - 3x + 1x - 3 = 0 \] Factor by grouping:
\[ x(x - 3) + 1(x - 3) = 0 \] \[ (x + 1)(x - 3) = 0 \] Now, set each factor to zero to find the values of x.
\[ x + 1 = 0 \implies x = -1 \] \[ x - 3 = 0 \implies x = 3 \]

Step 4: Final Answer:
The zeroes of the polynomial are -1 and 3. This matches option (B).