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If the sum of the slopes of the lines given by x² − 2cxy − 7y² = 0 is four times their product, c has the value

1. −2
2. −1
3. 2
4. 1

Correct answer: 2

Solution

The relationship between the sum and product of the slopes of the lines represented by the quadratic equation can be derived from the coefficients of the equation. In this case, setting the sum of the slopes equal to four times their product leads to a specific value for c, which is found to be 2.

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