Find m if the line y=mx−2 intersects y=x^2 in just one point.
Accepted Solution
A:
we have that y=mx−2 y=x²
if the line intersects a the parabola in one point so mx-2=x²-------> x²-mx+2=0 Find the discriminant D=b²-4ac a=1 b=-m c=2 D=m²-8 we know that
If D is negative ------> Then the square root is imaginary and there is no solution If D is 0 then there is exactly one solution if D is positive there are two solution therefore equals D to zero m²-8=0-------> m=(+/-)√8