The parabola y = 2x & # 178; - 3x + m has two intersection points with the straight line y = - 3x + 1 If M = - 1, find the length of the line cut by the parabola?

The parabola y = 2x & # 178; - 3x + m has two intersection points with the straight line y = - 3x + 1 If M = - 1, find the length of the line cut by the parabola?

(1) Parabola y = 2x & # 178; - 3x + M
The straight line y = - 3x + 1 is brought into the parabola and moves to the right direction
2x²+m-1=0
x²=1-m/2
There are two intersections
So 1-m / 2 > 0 is enough
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