Question

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If n²+2n-8 is a prime number where n€N, then n is -

A. also a prime no.
B. Relatively prime to 10.
C. Relatively prime to 6.
D. A composite no.

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Need a proper solution❕

Answer 1

solution :

Here we have to find the zeroes of the polynomial.

$= > {n}^{2} + 2n - 8 \\ = > {n}^{2} + 4n - 2n - 8 \\ = > n(n + 4) - 2(n + 4) \\ = > (n - 2)(n + 4) \\ = > n = 2or \: n = - 4$
Here,, it is given N is element of a natural number.

so; -4 is rejected.

hence, n = 2

We know that 2 is a prime numbere.

so, option A is correct.
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Now,
✴Factors of 10 = 1 , 2 , 5 & 10
✴Factors of 6 = 1 , 2 , 3 &6

We can se that 2 is the highest common factor of 10 and 6

so, it is relatively prime to 10 & 6 both.






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Hope it helps☺

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