Quadratic equations

Question

Write the quadratic equation in the form of ax²+bx + c=0 with the roots d abd f.

Answer 1

0 = (x-d)(x-f)

0 = x^2 -dx-fx +df

0 = ax^2 +bx +c where a=1,b=-d-f,c=df

0 = x^2 +(-d-f)x + df is the simplest quadrat with those two roots, d and f

but

there are an infinite number of other quadratics where a does not =1

let a be any real number, such as a=2

then

2x^2 +(-2d-2f)x + 2df =0 is another quadratic with the same two zeros d and f