JEE Advanced 2020 Full Test 4 Paper 1

x4+4x3−8x2=−k
⇒‌‌f(x)=−k
Where
f(x)=x4+4x3−8x2=x2(x2+4x−8)
Let g(x)=−k
From the graph the following cases arise :
1. When −3≤−k≤0,⇒0≤k≤3
In this case, y=−k intersect at four points.
2. When −4≤−k<−3,⇒3<k≤4
In this case, y=−k intersect at two points, the given equation has two real roots.
3. When k<0,⇒−k>0
In this case, there are two points of intersection. So, the equation has two real roots.