If the lines represented by the equation 6x^2 + 5xy + y^2 = 0 intersect at the o

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Question: If the lines represented by the equation 6x^2 + 5xy + y^2 = 0 intersect at the origin, what is the sum of their slopes?

Options:

Correct Answer: 0

Solution:

The sum of the slopes of the lines is given by -b/a, which is 0 in this case.

If the lines represented by the equation 6x^2 + 5xy + y^2 = 0 intersect at the origin, what is the sum of their slopes?

If the lines represented by the equation 6x^2 + 5xy + y^2 = 0 intersect at the origin, what is the sum of their slopes?

Correct Answer: 0

Step 1: Identify the given equation, which is 6x^2 + 5xy + y^2 = 0.
Step 2: Recognize that this is a quadratic equation in two variables (x and y) that can represent two lines.
Step 3: Rewrite the equation in the standard form of a quadratic equation: Ax^2 + Bxy + Cy^2 = 0, where A = 6, B = 5, and C = 1.
Step 4: Use the formula for the sum of the slopes of the lines represented by the equation, which is -B/A.
Step 5: Substitute the values of B and A into the formula: -B/A = -5/6.
Step 6: Calculate the result: -5/6 is the sum of the slopes of the lines.

Quadratic Equations – Understanding how to analyze and factor quadratic equations to find the slopes of intersecting lines.
Slope of Lines – Using the relationship between the coefficients of a quadratic equation to determine the slopes of the lines it represents.
Intersection at the Origin – Recognizing that if lines intersect at the origin, their slopes can be derived from the quadratic equation.