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Gala2k [10]
3 years ago
10

Using the factorised trinomial

(n-2)(4n-7)" align="absmiddle" class="latex-formula">, prove that there are only two values of n for which 4 n^{2} - 15n + 14 is a prime number.
Mathematics
1 answer:
andrew-mc [135]3 years ago
5 0
4n² - 15n + 14<span> is always the product of two numbers, for it to be prime number, one of these factors must be either 1 or -1.

Case n - 2 = 1
That would be n = 3
Then </span>4n² - 15n + 14<span> = 5 , which is prime.

Case n - 2 = -1
That would be n = 1
Then </span>4n<span>² - 15n + 14 = 3, which is also prime.

Case 4n - 7 = 1
That would be n = 2 and that makes other factor (n-2) zero so it's not prime

Case 4n-7 = -1
That would be n = 3/2 which is not integer, so </span>4n<span>² - 15n + 14 will not be interger.

For any other n values, </span>4n<span>² - 15n + 14 will be composite number since it is product of two factors.

Therefore we are left with n = 1 and n = 3; only two values of n.</span>
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