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

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Answer 1 · 2017-01-11T21:23:03

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

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.