Question

I need step by step analysis to do this quadratic inequality since im new to it.


A)Find the max value of k for which x^2 - 6x + k has real and distinct roots.

B) Find m for which x^2 -mx +4 has real and equal roots.

Answer 1

I think that you want equation instead of inequality.

For A) you require a number k such that x would equal a number that is both real and distinct. Basically you want to find an easy way to factor A.

If you make up a factor that lets the first two parts of A work then you get (x-5)(x-1) This leads to x^2-6x+5 The roots would be 5 and 1 which are both real and distinct. Therefore, my answer was k=5.

For B it is basically the same idea but they give you the first and third parts and ask for m.

The easiest way to get this answer is to think about what times what = 4. But of course, they have to be equal. Therefore, x^2 =4. Well, x= 2 or -2.

Therefore: (x-2)(x-2) = x^2-4x+4

Therefore: My answer is 4 because you put the question down as -m and if -m=-4 then m=4.

Answer 2

Thank you very much ! I really appreciate your time and effort into explaining fully ! Thank you :)

Answer 3

@Acer100 do you know the discriminant of a quadratic equation?

Answer 4

@Acer100 i don't agree with @malicals solution in part A.