Search any question & find its solution
Question:
Answered & Verified by Expert
If " $2 i$ " is a root of $f(z)=z^4+z^3+2 z^2+4 z-8=0$, then which among the following cannot be a root of $f(z)=0$ ?
Options:
Solution:
1984 Upvotes
Verified Answer
The correct answer is:
2
It is given that, $f(z)=z^4+z^3+2 z^2+4 z-8$ have a root $2 i$, so one more root will be $-2 i$, so $\left(z^2+4\right)$ is the factor of $z^4+z^3+2 z^2+4 z-8$.
So, $z^4+z^3+2 z^2+4 z-8$
$$
=\left(z^2+4\right)\left(z^2+z-2\right)
$$
and $z^2+z-2=(z+2)(z-1)$
Therefore, the roots of $f(z)$ are $2 i,-2 i,-2$ and 1 .
So, $z^4+z^3+2 z^2+4 z-8$
$$
=\left(z^2+4\right)\left(z^2+z-2\right)
$$
and $z^2+z-2=(z+2)(z-1)$
Therefore, the roots of $f(z)$ are $2 i,-2 i,-2$ and 1 .
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.