### Video Transcript

Determine the type of the roots of the equation four ๐ฅ times ๐ฅ plus five equals negative 25.

In order to determine these type of roots, we can look at the discriminant, which is ๐ squared minus four ๐๐. If it ends up being less than zero, it will have two different complex and nonreal roots. If ๐ squared minus four ๐๐ ends up being equal to zero, it will have two real and equal roots. And if itโs greater than zero, it will have two different real roots.

This comes from the quadratic formula, ๐ squared minus four ๐๐. So if you think about โ you know if you get a number underneath the square root and itโs less than zero, that means itโs negative. So youโre gonna have complex imaginary numbers that youโre gonna be working with.

If it would be equal to zero, the square root would completely disappear and youโre gonna have an answer thatโs just one answer because the square has disappeared. So itโs just gonna be whatever the fraction is. And then if itโs greater than zero, itโs gonna be some positive number and it may be a perfect square or it may be a nonperfect square. It just depends.

So thatโs where we get these from. So the first thing that we need to do is to distribute four ๐ฅ. And now we should add 25 to both sides. So we have four ๐ฅ squared plus 20๐ฅ plus 25 equals zero. Therefore, ๐ is four, ๐ is 20, and ๐ is 25.

Therefore, ๐ squared minus four ๐๐ will be equal to 20 squared minus four times four times 25, which is 400 minus 400, which is equal to zero. So we will have real and equal roots.