where a ≠ 0. (For a = 0, the equation becomes a linear equation.)

The letters a, b, and c are called coefficients: the quadratic coefficient a is the coefficient of x2, the linear coefficient b is the coefficient of x, and c is the constant coefficient, also called the free term or constant term.

Quadratic equations are called quadratic because quadratus is Latin for “square”; in the leading term the variable is squared.

ax^2 + bx + c = 0

It is also true that the sum of the roots (or solutions) is equal to -b/a while the product of the roots is c/a. So we add the two solutions you gave, and we get (3+3)/2 = 6/2 = 3. Next we multiply them, and we get (9 – 5)/4 = 1.

Therefore, -b/a = 3 and c/a = 1. If we let a = 1, we get b = -3 and c = 1. So the quadratic equation would be:

x^2-3x+1=0

Hope this helps.

Then, the quadratic equation is given by ax^2 -(sum)x + (product) = 0, a = non-zero constant.

TEH (Maths lecturer)

B = -3

A = 1

C = 1

So

x^2-3x+1=0

or

x^2-3x=-1