If a quadratic equation has roots 2 and -3, what is the equation in standard form?
Correct Answer: x^2 + x - 6 = 0
- Step 1: Identify the roots of the quadratic equation. The roots given are 2 and -3.
- Step 2: Write the factors of the equation using the roots. For root 2, the factor is (x - 2). For root -3, the factor is (x + 3).
- Step 3: Combine the factors into one equation: (x - 2)(x + 3) = 0.
- Step 4: Expand the equation by multiplying the factors: (x - 2)(x + 3) = x^2 + 3x - 2x - 6.
- Step 5: Simplify the equation: x^2 + 3x - 2x - 6 = x^2 + x - 6.
- Step 6: Write the final equation in standard form: x^2 + x - 6 = 0.
- Quadratic Equations – Understanding how to form a quadratic equation from its roots.
- Factoring – Using the roots to create factors and then expanding them to standard form.
- Standard Form of a Quadratic – Recognizing the standard form of a quadratic equation as ax^2 + bx + c = 0.
