Question

Under what circumstance can the quadratic function not be written in factored form

Answer 1

When the discriminant of a quadratic function is negative than it is not be written in factored form.

Explanation:

If a quadratic function is
`f(x)=ax^2+bx+c`, then

1. It is factorable if
`D=b^2-4ac\geq 0,` i.e., graph of function intersect the x-axis, roots of the function are real.

2. It is not factorable if
`D=b^2-4ac< 0,` i.e., graph of function does not intersect the x-axis, roots of the function are imaginary or complex.

It means, the quadratic function not be written in factored form when the discriminant of a quadratic function is negative.