If the lines represented by the equation 6x^2 - 5xy + y^2 = 0 are perpendicular,

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Question: If the lines represented by the equation 6x^2 - 5xy + y^2 = 0 are perpendicular, what is the value of 6?

Options:

Correct Answer: False

Solution:

The lines are not perpendicular as the condition for perpendicularity is not satisfied.

If the lines represented by the equation 6x^2 - 5xy + y^2 = 0 are perpendicular, what is the value of 6?

If the lines represented by the equation 6x^2 - 5xy + y^2 = 0 are perpendicular, what is the value of 6?

Step 1: Understand that the equation 6x^2 - 5xy + y^2 = 0 represents two lines.
Step 2: Recall that for two lines to be perpendicular, the product of their slopes must equal -1.
Step 3: Identify the coefficients in the equation: A = 6, B = -5, C = 1.
Step 4: Use the formula for the slopes of the lines derived from the equation: m1 and m2 can be found using the quadratic formula.
Step 5: Calculate the slopes using the discriminant method or by finding the roots of the equation.
Step 6: Check if the product of the slopes (m1 * m2) equals -1.
Step 7: Conclude that since the condition for perpendicularity is not satisfied, the lines are not perpendicular.

Quadratic Equations and Lines – Understanding how to analyze the roots of a quadratic equation to determine the nature of the lines it represents.
Perpendicular Lines Condition – Knowing the condition for two lines to be perpendicular, which involves the slopes of the lines.