Select Goal &
City
Select Goal
Explore
Question:
If f(z)=zn+an-1zn-1 +......+a1zn+a0 ∈ R[z] is a polynomial in z with no root over R,then deg(f)is
If f(z)=zn+an-1zn-1 +......+a1zn+a0 ∈ R[z] is a polynomial in z with no root over R,then deg(f)is
Updated On: Aug 19, 2024
- 9
- always≤4
- an odd number
- always≥4
- an even number
Hide Solution
Verified By Collegedunia
The Correct Option is
Solution and Explanation
The correct option is (E): an even number
Was this answer helpful?
1
1
Top Questions on complex numbers
- If \(r = |z|,\ θ = arg(z)\) and \( z = 2 – 2\ tan (\frac {5\pi}{8})\) then find \((r, θ)\).
- JEE Main - 2024
- Mathematics
- complex numbers
- If \(z = x + iy, \quad xy \neq 0\) satisfies the equation \(z^2 + iz = 0\), then \(|z^2|\); equal to
- JEE Main - 2024
- Mathematics
- complex numbers
- Let \(z_1\) and \(z_2\) be two complex numbers such that \(z_1 + z_2 = 5\) and \(z_1^3+z_2^3 =20 +15i\), then the value of \(| z_1^4+z_2^4 |\) is equal to
- JEE Main - 2024
- Mathematics
- complex numbers
- Let f(x) = x4 + ax3 + bx2 + c be a polynomial with real coefficients such that f(1) = -9. Suppose that \(i\sqrt3\) is a root of the equation 4x3 + 3ax2 + 2bx = 0, where\(i=\sqrt{-1}\) . If a1, a2, a3 and a4 are all the roots of the equation f(x) = 0, then |a1|2 + |a2|2 + |a3|2 + |a4|2 is equal to ______.
- JEE Advanced - 2024
- Mathematics
- complex numbers
- If : \(|z + 1| = αz + ß(i + 1)\) and \(z = \frac 12 - 2i\), find \(α + ß\).
- JEE Main - 2024
- Mathematics
- complex numbers
View More Questions
Questions Asked in KEAM exam
The angle of minimum deviation for a prism of apex angle 60° and refractive index of \(\sqrt{2}\) is:
- KEAM - 2023
- Ray optics and optical instruments
- A thin particle moves from \((0,1)\) and gets reflected upon hitting the x-axis at \((√3,0)\). Then the slope of the reflected line is ?
- KEAM - 2023
- Slope of a line
- Suppose \(A=\begin{bmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{bmatrix}\) is an adjoint of the matrix \(\begin{bmatrix} 1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4\end{bmatrix}\). Then the value of \(\frac{a_!+b_2+c_3}{b_1a_2}\) is
- KEAM - 2023
- Matrices
- Let \(k\) be a real number such that \(\sin \dfrac{3π}{14} \cos \dfrac{3π}{14} = k \cos \dfrac{π}{14}\).Then the value of \(4k\) is
- KEAM - 2023
- Trigonometry
- An average frictional force of 80N is required to stop an object at a distance of 25m. If the initial speed of the object is 20m/s,the mass of the object is:
- KEAM - 2023
- work, energy and power
View More Questions
SUBSCRIBE TO OUR NEWS LETTER
COLLEGE NOTIFICATIONSEXAM NOTIFICATIONSNEWS UPDATES
Download the Collegedunia app on 
© 2024 Collegedunia Web Pvt. Ltd. All Rights Reserved