How do you write the quadratic equation whose roots are n and -3n?

1 Answer
Jan 11, 2017

Answer:

#x^2+2nx-3n^2 = 0#

Explanation:

Let:

#f(x) = (x-n)(x+3n) = x^2+2nx-3n^2#

Then #f(x) = 0# if and only if at least one of #(x-n) = 0# or #(x+3n) = 0#

That is, if and only if #x=n# or #x=-3n#

So a suitable quadratic equation would be:

#x^2+2nx-3n^2 = 0#

Any quadratic equation in #x# with these zeros is a non-zero scalar multiple of this equation.