mx^2+12x+9m=0. for what values of m will the equation have one repeated root?
I can't remember how to calculate double root values
quadratic have double, or equal roots when the discriminant is zero
i.e.
b^2 - 4ac = 0
12^2 - 4m(9m) = 0
144 = 36m^2
m^2 = 4
m = ± 2
To find the values of m for which the equation has one repeated root, you need to consider the discriminant of the quadratic equation.
The discriminant is given by the formula:
Δ = b^2 - 4ac
For the equation mx^2 + 12x + 9m = 0, the coefficients are a = m, b = 12, and c = 9m.
Substituting these values into the discriminant formula, we have:
Δ = (12)^2 - 4(m)(9m) = 144 - 36m^2 = 0
Now we can solve this equation to find the values of m:
144 - 36m^2 = 0
Divide both sides by 36:
4 - m^2 = 0
Rearrange the equation to isolate m^2:
m^2 = 4
Take the square root of both sides to find the possible values of m:
m = ±2
Therefore, the values of m for which the equation has one repeated root are m = 2 and m = -2.