Question

Find all solutions to the following quadratic congruences by first making the lead coefficient 1 , then making the linear coefficient even, and finally by completing the square.

(a) 4x²+x+1≡0(mod7)

Answer 1

The quadratic congruence 4x²+x+1≡0(mod 7) is solved by first finding the multiplicative inverse of the lead coefficient modulo 7, then completing the square to find that x ≡ 4 (mod 7) are the solutions to the congruence.

Step-by-step explanation:

To solve the quadratic congruence 4x²+x+1≡0(mod 7), we want to make the lead coefficient 1 and the linear coefficient even before completing the square: