Question

The roots of the quadratic equation $x^2 + 5x + 6 = 0$ will be :

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

Hint:

If all coefficients in the quadratic equation are positive, the roots will be negative.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Roots of a quadratic equation are values of $x$ that satisfy the equation. This can be solved by factorizing the middle term.
Step 2: Factoring the Equation:
Find two numbers that multiply to 6 and add to 5. These are 2 and 3. \[ x^2 + 3x + 2x + 6 = 0 \] \[ x(x + 3) + 2(x + 3) = 0 \] \[ (x + 3)(x + 2) = 0 \]
Step 3: Solving for Roots:
Setting each factor to zero:
$x + 3 = 0 \implies x = -3$
$x + 2 = 0 \implies x = -2$
Step 4: Final Answer:
The roots are -3 and -2.