Problem 772
Prove that the function \(\displaystyle x^5 -5x +2\) has 3 real roots. Difficulty: 3. |
Problem 773
Prove that the function \(\displaystyle x^7+8x^2 +5x-23\) has at most 3 real roots. Difficulty: 3. |
Problem 775
For which values of \(\displaystyle k\) does the function \(\displaystyle x^3-6x^2+9x+k\) have exactly one real root? Difficulty: 4. |
Problem 774
At most how many real roots does the function \(\displaystyle x^{16} +ax+b\) have? Difficulty: 5. |
Problem 776
At most how many real roots does the function \(\displaystyle e^x+p(x)\) have, if \(\displaystyle p\) is a polynomial of degree \(\displaystyle n\)? Difficulty: 8. |
Supported by the Higher Education Restructuring Fund allocated to ELTE by the Hungarian Government |