If the lines represented by the equation 2x^2 + 3xy + y^2 = 0 intersect at the o

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Question: If the lines represented by the equation 2x^2 + 3xy + y^2 = 0 intersect at the origin, what is the sum of the slopes?

Options:

Correct Answer: -3

Solution:

The sum of the slopes of the lines can be found using the relation -b/a, which gives -3.

If the lines represented by the equation 2x^2 + 3xy + y^2 = 0 intersect at the origin, what is the sum of the slopes?

If the lines represented by the equation 2x^2 + 3xy + y^2 = 0 intersect at the origin, what is the sum of the slopes?

Step 1: Identify the given equation, which is 2x^2 + 3xy + y^2 = 0.
Step 2: Recognize that this equation represents two lines that intersect at the origin (0,0).
Step 3: Rewrite the equation in the standard form of a quadratic equation in terms of y: y^2 + 3xy + 2x^2 = 0.
Step 4: Identify the coefficients a, b, and c from the standard form: a = 2, b = 3, c = 1.
Step 5: Use the formula for the sum of the slopes of the lines, which is -b/a.
Step 6: Substitute the values of b and a into the formula: -3/2.
Step 7: Calculate the result: -3/2 = -3.

Quadratic Equations – Understanding how to analyze and factor quadratic equations to find the slopes of intersecting lines.
Slope of Lines – Using the relationship between coefficients in a quadratic equation to determine the slopes of the lines.
Intersection of Lines – Recognizing that the lines intersect at the origin and how this affects the calculation of slopes.