For the lines represented by the equation 5x^2 + 6xy + 5y^2 = 0, what is the sum

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

Options:

Correct Answer: -6/5

Solution:

The sum of the slopes is given by - (coefficient of xy)/(coefficient of x^2) = -6/5.

For the lines represented by the equation 5x^2 + 6xy + 5y^2 = 0, what is the sum of the slopes?

For the lines represented by the equation 5x^2 + 6xy + 5y^2 = 0, what is the sum of the slopes?

Correct Answer: -6/5

Step 1: Identify the equation given, which is 5x^2 + 6xy + 5y^2 = 0.
Step 2: Recognize that this is a quadratic equation in two variables (x and y).
Step 3: Identify the coefficients in the equation: the coefficient of x^2 is 5, the coefficient of xy is 6.
Step 4: Use the formula for the sum of the slopes of the lines represented by the equation, which is - (coefficient of xy) / (coefficient of x^2).
Step 5: Substitute the values into the formula: - (6) / (5).
Step 6: Simplify the expression to get -6/5.
Step 7: Conclude that the sum of the slopes is -6/5.

Quadratic Equations – Understanding how to analyze and manipulate quadratic equations in two variables.
Slope of Lines – Knowing how to derive slopes from the coefficients of a quadratic equation.
Sum of Slopes – Calculating the sum of slopes of lines represented by a quadratic equation.