we want solutions to
3x^2 - 6x + 7 = mx - 5
3x^2 - (m+6)x + 12 = 0
This has a single root (meaning the line is tangent to the parabola) when
(m+6)^2 - 144 = 0
m^2 + 12m - 108 = 0
m = -18 or 6
In between -18 and 6, the discriminant is negative, meaning there is no solution, meaning the line does not touch the parabola.
So, for m in (-18,6) the line does not touch the parabola
If the line y=mx-5 does not meet the curve y=3x^2-6x+7 then value of m is in the open interval (a,b).
Find the exact value of b.
1 answer
1 answer