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There is an integer n such that 2n2 − 5n + 2 is prime. To prove the statement it suffices to find a value of n such that (n, 2n2 − 5n + 2) satisfies the property "2n2 − 5n + 2 is prime." Show that you can do this by entering appropriate values for n and 2n2 − 5n + 2.

Respuesta :

amna04352

Answer:

n = 0 or 3

Step-by-step explanation:

2n² - 5n + 2

2n² - 4n - n + 2

2n(n - 2) -1(n - 2)

(n - 2)(2n - 1)

Prime number is one which is divisible by itself and 1

n-2 = 1 n = 3

2n-1 = 1 n = 0

abidemiokin

The required integer n that will make the expression prime is 4

Given the following quadratic expression  2n² − 5n + 2

To prove the statement it suffices to find a value of n such that (n, 2n² − 5n + 2) satisfies the property "2n² − 5n + 2 is prime, we will need to factorize the quadratic expression:

By factorizing

[tex]2n^2 - 5n + 2[/tex]

[tex]=2n^2 -4n -n + 2\\=2n(n-2)-1(n-2)\\=(2n-1)(n-2)\\[/tex]

Equate the factors to 2 (since 2 is a prime number ) and find n:

2n - 1 = 2

2n = 3

n = 3/2

n - 2 = 2

n = 2 + 2

n = 4

Hence the required integer n that will make the expression prime is 4

Learn more here; https://brainly.com/question/14802854

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