metadata
base_model: AI-MO/NuminaMath-7B-TIR
license: apache-2.0
pipeline_tag: text-generation
tags:
- alignment-handbook
- generated_from_trainer
- llama-cpp
- gguf-my-repo
widget:
- example_title: Math problem
messages:
- role: user
content: >-
For how many values of the constant $k$ will the polynomial
$x^{2}+kx+36$ have two distinct integer roots?
output:
text: >-
### Solution:
1- For the polynomial \\( x^2 + kx + 36 \\) to have two distinct integer
roots, let's denote these roots by \\( r_1 \\) and \\( r_2 \\).
2- According to Vieta's formulas, the sum of the roots \\( r_1 + r_2 \\)
is equal to \\(-k\\), and the product of the roots \\( r_1 \\cdot r_2
\\) is equal to 36.
3- To find the distinct integer pairs \\((r_1, r_2)\\) whose product is
36, we need to determine all pairs of integers \\((r_1, r_2)\\) such
that \\( r_1 \\cdot r_2 = 36 \\) and \\( r_1 \\neq r_2 \\).
4- From the equation \\( r_1 + r_2 = -k \\), for each valid pair
\\((r_1, r_2)\\), we can compute the corresponding value of \\( k \\).
5- Finally, since we need the polynomial to have two distinct integer
roots, we need to ensure that \\( r_1 \\) and \\( r_2 \\) are distinct.
Let's start by finding all pairs \\((r_1, r_2)\\) such that \\( r_1
\\cdot r_2 = 36 \\). We'll then determine the values of \\( k \\) and
ensure the roots are distinct.
```python import itertools
# Find all pairs (r1, r2) such that r1 * r2 = 36 product_36 = 36
factor_pairs = []
for i in range(1, product_36 + 1):
if product_36 % i == 0:
pair = (i, product_36 // i)
if pair[0] != pair[1]: # Ensure distinct pairs
factor_pairs.append(pair)
# Calculate k for each pair and ensure distinct integer roots
valid_k_values = set()
for r1, r2 in factor_pairs:
if r1 != r2:
k = -(r1 + r2)
valid_k_values.add(k)
print((len(valid_k_values), sorted(valid_k_values)))
```
```output
(4, [-37, -20, -15,-13])
```
The distinct integer values of \\( k \\) that make the
polynomial \\( x^2 + kx + 36 \\) have two distinct integer roots are
\\(-37, -20, -15, \\text{and} -13\\).
Therefore, the number of such values of \\( k \\) is:
[ \\boxed{4} \\]
model-index:
- name: NuminaMath-7B-TIR
results: []
kawchar85/NuminaMath-7B-TIR-Q6_K-GGUF
This model was converted to GGUF format from AI-MO/NuminaMath-7B-TIR using llama.cpp via the ggml.ai's GGUF-my-repo space.
Refer to the original model card for more details on the model.
Use with llama.cpp
Install llama.cpp through brew (works on Mac and Linux)
brew install llama.cpp
Invoke the llama.cpp server or the CLI.
CLI:
llama-cli --hf-repo kawchar85/NuminaMath-7B-TIR-Q6_K-GGUF --hf-file numinamath-7b-tir-q6_k.gguf -p "The meaning to life and the universe is"
Server:
llama-server --hf-repo kawchar85/NuminaMath-7B-TIR-Q6_K-GGUF --hf-file numinamath-7b-tir-q6_k.gguf -c 2048
Note: You can also use this checkpoint directly through the usage steps listed in the Llama.cpp repo as well.
Step 1: Clone llama.cpp from GitHub.
git clone https://github.com/ggerganov/llama.cpp
Step 2: Move into the llama.cpp folder and build it with LLAMA_CURL=1 flag along with other hardware-specific flags (for ex: LLAMA_CUDA=1 for Nvidia GPUs on Linux).
cd llama.cpp && LLAMA_CURL=1 make
Step 3: Run inference through the main binary.
./llama-cli --hf-repo kawchar85/NuminaMath-7B-TIR-Q6_K-GGUF --hf-file numinamath-7b-tir-q6_k.gguf -p "The meaning to life and the universe is"
or
./llama-server --hf-repo kawchar85/NuminaMath-7B-TIR-Q6_K-GGUF --hf-file numinamath-7b-tir-q6_k.gguf -c 2048