Question

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Solve 3x2 + 9x + 7 = 0 (mod 13)​

Answer 1

Answer:

The answer is 3 x 16 + 43 = 91 = 0 (mod 13)

Step-by-step explanation:

3 x^2 + 9 x + 7 = 0(mod 13)  

Let's multiply by 9(the inverse of 3) to get rid of the 3.

x^2 + 3 x + 11 = 0(mod 13)  

Now write this as  :

x^2 -10 x + 11 = 0(mod 13)  

Complete the square:

x^2 -10 x + 25 -1 = 0(mod 13)

(x-5)^2 = 1(mod 13)  

Solve  

x -5 = 1(mod 13, x = 6(mod 13)

x-5 = 12(mod 13), x = 4(mod 13)

Check the work:

3 x 36 + 54 + 7 = 169 = 0(mod 13)  

3 x 16 + 43 = 91 =0(mod 13)

Answer 2

Answer:

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