Find a quadratic equation in standard form with real coefficients that has the given solution .
a.1-2i
b.-2-i

Question

Find a quadratic equation in standard form with real coefficients that has the given solution .
a.1-2i
b.-2-i

dape · Answer

Start from the polynomial corresponding to the equation in factored form, that is let's say we know one solution is $-3$ and the other is $\sqrt{2}$, then we know
$$ (x-(-3))(x-\sqrt{2})=0 $$
Because if we put in the solutions we will get 0 in both cases. Now, if we expand the left hand side we get a quadratic equation with these solutions!

dape · Answer

So in my example the quadratic formula with solutions $-3$ and $\sqrt{2}$ is
$$ x^2+x(3-\sqrt{2})-3\sqrt{2}=0 $$

anonymous · Answer

So how do I start with my problems?

dape · Answer

Write the solutions as factors. A hint is that the first factor is $(x-(1-2i))$

anonymous · Answer

Okay now I have x,-1+2i