The product of the roots of the quadratic equation x^2 + 5x + 6 = 0 is: (2021)

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Question: The product of the roots of the quadratic equation x^2 + 5x + 6 = 0 is: (2021)

Options:

Correct Answer: 6

Exam Year: 2021

Solution:

The product of the roots is given by c/a = 6/1 = 6.

The product of the roots of the quadratic equation x^2 + 5x + 6 = 0 is: (2021)

The product of the roots of the quadratic equation x^2 + 5x + 6 = 0 is: (2021)

Step 1: Identify the quadratic equation. The given equation is x^2 + 5x + 6 = 0.
Step 2: Recognize the standard form of a quadratic equation, which is ax^2 + bx + c = 0.
Step 3: Identify the coefficients a, b, and c from the equation. Here, a = 1, b = 5, and c = 6.
Step 4: Use the formula for the product of the roots of a quadratic equation, which is given by c/a.
Step 5: Substitute the values of c and a into the formula. This gives us 6/1.
Step 6: Calculate the result of 6/1, which equals 6.
Step 7: Conclude that the product of the roots of the quadratic equation is 6.

Quadratic Equations – Understanding the standard form of a quadratic equation and how to find the product of its roots using the formula c/a.
Vieta's Formulas – Application of Vieta's formulas to relate the coefficients of a polynomial to sums and products of its roots.