for what real values of k do each of the follwoing quadratic equations have one double root? how do i do this?

Question

x^2-kx+36=0 can you explain what this means?

and...


for what real values of k do each of the following quadratic equations have 2 real and distinct roots? kx^2+x+1=0

Answer 1

A quadratic (ax²+bx+c=0) has roots defined by:

x = (-b±√(b²-4ac))/2a)

The roots will be equal when b²-4ac=0

In the case of the given equations:
x²-kx+36 will have double roots when k²-144=0 or k=±12

kx² + x + 1 = 0
x = (-1±√(1-4k))/2k)
The roots will be real and distinct if k<1/4

Answer 2

There's a double root R when the quadratic is Constant * (x-R)^2.

So it has to look like the template x^ - 2Rx + R^2.

Here R^2 has to be 36, so R has to be +/- 6. So k has to be +/-12.

Answer 3

only thing i know is that the roots are imaginary cause plus 36 would make that the y interccept and make the quadratic not touch the x axis so youd have to do more math to find out the coordinates for the root.