For what value of t does the line (3t^2 + 2t)x - y = 21 not intersect the line x + y = 1

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justaguide | College Teacher | (Level 2) Distinguished Educator

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If two lines do not intersect each other, they have an equal slope. The slope of the line (3t^2 + 2t)x - y = 21 is 3t^2 + 2t. The slope of the line x + y = 1 is -1.

As the two lines are parallel to each other, 3t^2 + 2t = -1

3t^2 + 2t = -1

=> 3t^2 + 2t + 1 = 0

=> t = `(-2+-sqrt(4 - 12))/(6)`

The values of t are imaginary.

There is no real value of t for which the given condition is satisfied.

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