If $f(x) \in \mathbb{Q}[x]$ is a non-zero polynomial such that all its roots are irrational,then the degree of $f(x)$ is

  • A
    an even number
  • B
    an odd number
  • C
    $0$
  • D
    cannot be determined

Explore More

Similar Questions

If the roots of the equation $6x^2 - 7x + k = 0$ are rational,then $k = .......$

Solve the equation $x^{2}-2x+\frac{3}{2}=0$.

The sum of the roots of the equation $x^2 + |2x - 3| - 4 = 0$ is:

If for any real $x$,$y = \frac{11 x^2+12 x+6}{x^2+4 x+2}$ is such that $y < a$ or $y \geq b$,then $a, b$ are

What is the remainder of $2x^3 - 5x^2 + 7$ when divided by $(x - 2)$?

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo