If a quadratic equation has roots 2 and -3, what is the equation in standard for

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Question: If a quadratic equation has roots 2 and -3, what is the equation in standard form?

Options:

Correct Answer: x^2 + x - 6 = 0

Solution:

The equation can be formed as (x - 2)(x + 3) = 0, which expands to x^2 + x - 6 = 0.

If a quadratic equation has roots 2 and -3, what is the equation in standard form?

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.