If a quadratic equation has equal roots, then shouldn't the answer you get be the same numbers? REPOST

Ok, i'm going to write everything the question says,

The quadratic equation x^2+(m+4)x+(4m+1)=0, where m is constant has EQUAL ROOTS.
a)show that m2-8m+12=0
b)hence find the possible values of m

my question is the answer to Qb is m=6 or m=2, which aren't the same/equal but the question says they are supposed to be because it says "The quadratic equation where m is constant has equal roots." so what am I misunderstanding here?

You have misunderstood.
The question says that the roots of the quadratic in x are equal which means that after writing the quadratic equations with the found values of m, the values of x will be the same on solving which means that the quadratic equations will be perfect squares. Let us check this using m = 6 and m = 2
For m = 6, the quadratic equation is
x^2 + 10x + 25 = (x + 5)^2
=> (x + 5)^2 = 0 has two equal roots x = - 5 and x = - 5

For m = 2, the quadratic equation is
x^2 + 6x + 9 = (x + 3)^2
=> (x + 3)^2 = 0 has two equal roots x = - 3 and x = -3.

Explanation:
It is only the quadratic in x that has to have equal roots.
That means it is a perfect square and the determinant is zero.

This rule creates a condition amounting to a quadratic in m,
and that quadratic does NOT have to have equal roots, and is
m^2 - 8m + 12 = 0

If you substitute the two values of m, (m = 2 or 6),
that make the original equation have equal roots you get
x^2+(2+4)x+(4*2+1) = x^2 + 6x + 9 = (x + 3)^2 = 0
x^2+(6+4)x+(4*6+1) =x^2 + 10x + 25 = (x + 5)^2 = 0
and as you see these do have equal roots.

Regards - Ian

that means 2 values of x are same and not the 2 values of m

if m = 6 we get x^2+10x+25= 0 or (x+5)^2 = 0 or double root is - 5

if m = 2 we get x^2+6x+9 = 0 or (x+3)^2= 0 or double root x = - 3

x has double root for both the m's.