Question

What are all the roots of x2-4x+29=0

Answer 1

To solve a quadratic equation in the form
`ax^2+bx+c=0` you can use the quadratic formula:

`x_(1,2) = (-b\pm√(b^2-4ac))/(2a)`

In your case, the equation
`x^2-4x+29=0` is identified by the coefficient choice
`a=1,\ b=-4,\ c=29`, so the solving formula becomes

`x_(1,2) = (4\pm√(16-116))/(2) = (4\pm√(-100))/(2)`

As you can see, we have a negative number under a square root, an operation impossible to perform using real numbers. So, this equation has no real solutions.