roots of the equation x4+4x3-8x2+k=0 when
1. k = [0,3],are
a) all real.
b) two real two complex.
c) no real.
d) none.
2. k = (3,4],are
a) all real.
b) two real two complex.
c) no real.
d) coincident.
3. k = (-inf,0),are
a) all real.
b) two real two complex.
c) no real.
d) repeated roots.
4. k = (4,inf),are
a) all real.
b) two real two complex.
c) no real.
d) repeated roots.
11.a)
2.b)
3.b)
& either i'm making some horrible mistake and all these ans r wrong or there is some problem with the last question.....
11See the 1st sum will tell the whole story....
We have f(-1)<0, also f(0)>0, so that gives a root between (-1,0).
Also f(-1)\le 0, so there's a root in the interval (0,1]....Also as x→∞, f(x) becomes a positive number.....so that gives 3 roots - implying 4 real roots.
Same approach for the remaining ones.
341http://www.goiit.com/posts/list/algebra-quadratic-for-jee-comprehension-type-question-47960.htm
