Question

The roots of \(x^2+x-6=0\) are

• A. 2, -3
• B. -2,3
• C. 2, 3
• D. -2, -3

Answer 1

The Correct Option is A

To solve this problem, we need to find the roots of the quadratic equation:

1. Given Equation:
\[ x^2 + x - 6 = 0 \]

2. Factoring the Quadratic:
We look for two numbers whose product is -6 and sum is +1 (coefficient of x).
The numbers 3 and -2 satisfy this:
\[ 3 \times (-2) = -6 \quad \text{and} \quad 3 + (-2) = 1 \]

3. Writing the Factored Form:
\[ x^2 + x - 6 = (x + 3)(x - 2) = 0 \]

4. Solving for Roots:
Setting each factor to zero gives:
\[ x + 3 = 0 \Rightarrow x = -3 \]
\[ x - 2 = 0 \Rightarrow x = 2 \]

Final Answer:
Option (A) 2, -3 is correct.