Find m if the line y=mx−2 intersects y=x^2 in just one point.
1 answer:
We have that
<span>y=mx−2
y=x</span>²
if the line <span>intersects a the parabola in one point
so
mx-2=x</span>²-------> x²-mx+2=0
<span>Find the discriminant D=b</span>²-4ac
a=1
b=-m
c=2
D=m²-8
we know that
If D<span> is negative ------> Then the square root is imaginary and there is no solution
If </span>D<span> is </span>0<span> then there is exactly one solution
if </span>D<span> is positive there are two solution </span>
therefore
equals D to zero
m²-8=0-------> m=(+/-)√8
the answer is
m=(+/-)√8
see the attached figure
m has two solutions
<span>y=mx−2
y=x</span>²
if the line <span>intersects a the parabola in one point
so
mx-2=x</span>²-------> x²-mx+2=0
<span>Find the discriminant D=b</span>²-4ac
a=1
b=-m
c=2
D=m²-8
we know that
If D<span> is negative ------> Then the square root is imaginary and there is no solution
If </span>D<span> is </span>0<span> then there is exactly one solution
if </span>D<span> is positive there are two solution </span>
therefore
equals D to zero
m²-8=0-------> m=(+/-)√8
the answer is
m=(+/-)√8
see the attached figure
m has two solutions
You might be interested in
Answer: 49+64i
Step-by-step explanation:
Concept to know:
i=√-1
i²=-1
i³=-i
=1
-------------------------------------
(-5+8i)(3-8i)
=-15+40i+24i-64i²
=-15+64i-64i²
=-15+64i+64 (remember, i²=-1)
=49+64i
Hope this helps!! :)
Please let me know if you have any question or need further explanation