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