Register

GATE ECE 2013 | Question: 20

• retagged by
485 views
0 0 votes

A polynomial $f(x) = a_{4}x^{4} + a_{3}x^{3} + a_{2}x^{2} + a_{1}x - a_{0}$ with all coefficients positive has

  1. no real roots
  2. no negative real root
  3. odd number of real roots 
  4. at least one positive and one negative real root 

Please log in or register to answer this question.

Answer:
← Previous · GATE ECE 2013 | Ques...Next → · GATE ECE 2013 | Ques...
← Previous in category · GATE ECE 2012 | Ques...Next in category → · GATE ECE 2014 Set 1 ...
Position:
Show:
Voting & Accepting an answer helps improve the community

Related questions

1 1 vote
0 0 answers
329
329 views
admin asked Dec 12, 2022
329 views
TIFR ECE 2013 | Question: 19
Which of the following is true for polynomials defined over real numbers $\mathbb{R}$.Every odd degree polynomial has a real root.Every odd degree polynomial has at least...
1 1 vote
0 0 answers
326
326 views
admin asked Dec 14, 2022
326 views
TIFR ECE 2014 | Question: 20
What is\[\lim _{n \rightarrow \infty} \cos \frac{\pi}{2^{2}} \cos \frac{\pi}{2^{3}} \cdots \cos \frac{\pi}{2^{n}} ?\]$0$$\pi / 2$$1 / \sqrt{2}$$2 / \pi$None of the above.
1 1 vote
0 0 answers
282
282 views
admin asked Dec 12, 2022
282 views
TIFR ECE 2013 | Question: 20
A function $f: \mathbb{R} \rightarrow \mathbb{R}$ is convex if for $x, y \in \mathbb{R}, \alpha \in[0,1], f(\alpha x+(1-\alpha) y) \leq \alpha f(x)+(1-\alpha) f(y)$.Which...
1 1 vote
0 0 answers
417
417 views
admin asked Nov 30, 2022
417 views
TIFR ECE 2010 | Question: 20
The function $f(t)$ is a convolution of $t^{2}$ with $\exp \left(-t^{2} / 2\right) / \sqrt{2 \pi}$. Its derivative is$2 t$$t^{2}$$2 t+t e^{-t^{2} / 2}$Does not have a sim...

Add Synced Question

×