Question

What is the value of m, if the equation my2+2y−4=0 has exactly one root?

Answer 1

For the quadratic equation my₂ + 2y - 4 = 0 to have exactly one root, the discriminant must be zero, which leads to the calculation of m being -1/4.

Step-by-step explanation:

The equation my₂ + 2y - 4 = 0 will have exactly one root if its discriminant D = b₂ - 4ac is equal to zero. Here, a = m, b = 2, and c = -4. Therefore, the discriminant is D = 22 - 4(m)(-4).

Setting D to zero for a single root, we get 4 + 16m = 0, solving this gives m = -1/4.

Hence, the value of m for the equation to have exactly one root is -1/4.

Answer 2

`m=(-1)/(4)`

Step-by-step explanation:

A quadratic equation has one root if the discriminant is 0.

That is we need
`b^2-4ac=0` for this particular question.

Compare the following to find
`a,b, \text{ and } c`:

`ax^2+bx+c=0`

`my^2+2y-4=0`

The variable
`x` is representative of the variable
`y` here.

`a=m`

`b=2`

`c=-4`

Plug in into
`b^2-4ac=0`:

`(2)^2-4(m)(-4)=0`

`4+16m=0`

Subtract 4 on both sides:

`16m=-4`

Divide both sides by 16:

`m=(-4)/(16)`

Reduce:

`m=(-1)/(4)`