I keep googling it and I still don’t understand what they are and their differences 😭😭
In: 18
A quadratic equation is y = ax² + bx + c. How do you find a value for x, so that y will be 0? There’s a thing called the quadratic formula that does this for you. You take the numbers for a, b, and c, and put them in to this formula, and you’ll get the x you need to make y equal 0.
However, this quadratic formula has a square root. Sometimes the numbers you put into the formula mean that square root is for a negative number.
You can get the square root of say 25 which is 5. But what’s the square root of -25?
That’s where complex numbers step in. They let you say (i × 5) is the square root of -25. What is i? i is made up by mathematicians, to be the square root of -1. If you multiply i by itself – that is, square it – you’ll get -1. Or if you multiply (i × 5) by (i × 5), you’ll get (-1 × 25) = -25.
This lets you avoid shrugging and giving up when faced with negative square roots.
A real root is any time your quadratic formula has a positive square root. A non-real (aka complex) root is when your quadratic formula has a negative square root.
Edit: for accuracy’s sake, -5 is also a root of 25. And so, (i × -5) is also a root of -25. Handwaving to avoid adding extra complexity to this explanation, this is how you get two roots for the quadratic equation.
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