Identify a possible pair of values for a and c so that ax2−6x+c=0 has one real solution. Then write the equation

Question

Please also explain how you would solve it, because I am super lost and just looking for answers now but I would like to do it on my own, ideally.

Answer 1

in order to find this you must use the discriminant b^2-4ac (comes from what is under the square root in the quadratic formula), there are 3 situations you should know:

1) b^2-4ac > 0 ---> means there are 2 real solutions

2) b^2-4ac = 0 ---> means there is 1 real solution

3) b^2-4ac < 0 ---> means there are 2 imaginary solutions

in your case of ax^2-6x+c you are looking for one real solution so lets use the 2nd situation:

6^2-4ac = 0, 36-4ac = 0, 36 = 4ac, ac = 9 or a=9/c, in this case a can be 1 and c can be 9 as one pair, another is a can be 3 and c can be 3, you get the idea