What is the value of m, if the equation my^2+2y−4=0 has exactly one root?
Steve is correct, but it never specifies it has to be a quadratic equation, so m can also be 0.
To find the value of m, we need to consider the discriminant of the quadratic equation. The discriminant is given by:
Δ = b^2 - 4ac
Here, a = m, b = 2, and c = -4.
Since the equation has exactly one root, the discriminant should be equal to zero.
So, we have:
Δ = (2)^2 - 4(m)(-4)
0 = 4 - 16m
16m = 4
Dividing both sides by 16:
m = 4/16
m = 1/4
Therefore, the value of m is 1/4.
To find the value of m, we need to consider the discriminant of the quadratic equation. The discriminant is the part of the quadratic formula that appears under the square root sign.
In the given equation, my^2 + 2y - 4 = 0, we have the quadratic equation in the form ay^2 + by + c = 0, where a = m, b = 2, and c = -4.
The discriminant, denoted as Δ, is calculated using the formula Δ = b^2 - 4ac.
For the equation my^2 + 2y - 4 = 0, the discriminant is Δ = (2)^2 - 4(m)(-4).
Simplifying further, we get Δ = 4 + 16m.
Now, for the equation to have exactly one root, the discriminant must be equal to zero, Δ = 0. This means that there is only one unique solution for y, indicating that the quadratic equation has exactly one root.
Setting the discriminant to zero, we have 4 + 16m = 0.
Solving for m, we subtract 4 from both sides: 16m = -4.
Dividing both sides by 16, we find that m = -4/16 or m = -1/4.
Therefore, the value of m, if the equation my^2 + 2y - 4 = 0 has exactly one root, is m = -1/4.
to have one root, the discriminant must be zero. That is,
4+16m = 0