Teaching JKPSC Lecturership Mock Test Series 2024-25 Physical Sciences Mathematical Methods of Physics Complex Analysis
The roots of the polynomial, 𝑓(𝑧) = 𝑧4 − 8𝑧3 + 27z2 − 38𝑧 + 26, are 𝑧1, 𝑧2, 𝑧3, & 𝑧4, where 𝑧 is a complex variable. Which of the following statements is correct?
1
\( \frac{z_1+z_2+z_3+z_4}{z_1 z_2 z_3 z_4}=-\frac{4}{19} \)
2
\( \frac{z_1+z_2+z_3+z_4}{z_1 z_2 z_3 z_4}=\frac{4}{13}\)
3
\( \frac{z_1 z_2 z_3 z_4}{z_1+z_2+z_3+z_4}=-\frac{26}{27} \)
4
\( \frac{z_1 z_2 z_3 z_4}{z_1+z_2+z_3+z_4}=\frac{13}{19} \)