Question

Consider the equation $z^{10}+2z^5-15=0$

• A. Number of roots of the equation whose real part is positive is $5$
• B. Number of roots of the equation whose imaginary part is non negative is $5$
• C. Number of roots of the equation whose real part is negative is $5$
• D. Number of roots of the equation whose imaginary part is negative is $4$

Answer 1

Answer: (A), (C), (D)

The correct options are
A Number of roots of the equation whose real part is positive is $5$
C Number of roots of the equation whose real part is negative is $5$
D Number of roots of the equation whose imaginary part is negative is $4$

$z^{10}+2z^5-15=0(z^5+5)(z^5-3)=0\Rightarrow z^5=-5\text{or}3z=5^{\frac{1}{5}}{e}^{\frac{i(2n+1)\pi }{5}},3^{\frac{1}{5}}{e}^{\frac{i2n\pi }{5}}n\in \{0,1,2,3,4\}$
The roots of the above equation can be represented as: