Question

How do you factor quadratic equations when a is not 1?

Answer 1

See explanation.

Explanation:

If you have a quadratic equation:

`ax^2+bx+c=0`

then to factor it first you have to calculate the discriminant:

`Delta=b^2-4ac`

If the discriminant is negative then the equation has no real roots, so it cannot be factorised, else if it is greater than zero you can calculate two real roots using:

`x_{1,2}=(-b+-sqrt(Delta))/(2a)`

and factorise the equation to:

`a(x-x_1)(x-x_2)=0`

If the discriminant is zero, then the equation has 1 real root

`x_0=-b/(2a)`

and the factorisation is:

`a(x-x_0)^2=0`