Double/triple roots and imaginary roots

[glacial pulsar]

What's your question exactly?

If you're asking the meaning of double, triple and imaginary roots, a short explanation would be...

For the given ax² + bx + c = 0 quadratic equation, Δ = b² - 4ac (discriminant), and the solution would be x = (-b ∓ √Δ)/2a, a double root happens when Δ = 0, this implies that the given expression can be written in the form of (px + t)², a triple root means when you have 3 roots but they are all the same, this happens with cubic equations, given as ax³ + bx² + cx + d, this happens when the expression is in the form of (px + t)³, and finally the imaginary root is the solution that is out of the real numbers, we need the imaginary unit i for this which is √-1, this obviously is undefined in real number, that's why it's an element of Complex Numbers, for example, x² + 1 = 0, the roots of this equation is undefined in real numbers, however √-1 = i satisfies for this equation, which we call, an imaginary root.

Hope that helps.

[little vessel]

.solved