3 How many quadratic polynomials are there with coefficients

3. How many quadratic polynomials are there with coefficients mod 3? For each quadratic polynomial p with coefficients mod 3, write down all the solutions of p(x) = 0.

Solution

1. 7x²+4x-3=0

7x²+7x-3x-3=0

7x(x+1)-3(x+1)=0

(7x-3)(x+1)=0

x=3/7, x=-1

The solution for the quadratic polynomial with coefficient mod 3

2. 8x²+5x-3=0

8x²+8x-3x-3=0

8x(x+1)-3(x+1)=0

x=-1, =3/8

3.9x²+6x-3=0

9x²+9x-3x-3=0

9x(x+1)-3(x+1)=0

x=-1, x=3/9

4.10x²+7x-3=0

10x²+10x-3x-3=0

10x(x+1)-3(x+1)=0

x=-1, x=3/10

In this way, number of equations can be formed in the form

(n+3)x²+nx-3=0

Hence n number of quadratic polynomials can be formed with mo 3