For the quadratic equation x^2 + 6x + 8 = 0, what are the roots?
Correct Answer: -2 and -4
- Step 1: Start with the quadratic equation x^2 + 6x + 8 = 0.
- Step 2: Look for two numbers that multiply to 8 (the constant term) and add up to 6 (the coefficient of x).
- Step 3: The numbers 2 and 4 work because 2 * 4 = 8 and 2 + 4 = 6.
- Step 4: Rewrite the equation using these numbers: (x + 2)(x + 4) = 0.
- Step 5: Set each factor equal to zero: x + 2 = 0 and x + 4 = 0.
- Step 6: Solve for x in each equation: x = -2 and x = -4.
- Step 7: The roots of the equation are -2 and -4.
- Quadratic Equations – Understanding how to solve quadratic equations using factoring.
- Factoring – Recognizing how to factor a quadratic expression into two binomials.
- Roots of Equations – Identifying the solutions (roots) of a quadratic equation.
