Question

How do you write a quadratic equation in standard form with solutions 2+3i, 2-3i?

Answer 1

`x^2-4x+13=0.`

Explanation:

Let the roots of the reqd. qudr. eqn. be `alpha=2+3i, beta=2-3i.`

Then, `alpha+beta=4,` &, `alpha*beta=(2+3i)(2-3i)=4-9i^2=4+9=13.`

Therefore, the reqd. qudr. eqn. is given by `x^2-(alpha+beta)x+alpha*beta=0,.` i.e., `x^2-4x+13=0.`