How do you find the zeros, real and imaginary, of y=x2−5x+16 using the quadratic formula?

1 Answer
Ken C.
Feb 3, 2016

x=5+i√392 and x=5−i√392

Explanation:

The quadratic formula is: −b±√b2−4ac2a.

This is used to solve equations of the form y=ax2+bx+c, which is the same type of equation as y=x2−5x+16. We can see that for our example, a=1, b=−5, c=16. Plugging these guys into the formula,
−(−5)±√(−5)2−4(1)(16)2(1)

And simplifying,
5±√25−642

5±√−392

We now see we have an issue - a negative in the square root. That means both of our solutions will be imaginary, so to represent that, we take the √−1 (i) out of the square root to make it positive:
5±i√392

The next thing we look for is any way to simplify the square root. But √39 can't be simplified further, which means our solutions are:
x=5+i√392
x=5−i√392

Related questions
See all questions in Quadratic Formula
Impact of this question
1387 views around the world
You can reuse this answer
Creative Commons License