Respuesta :
Answer:
[tex]m=\frac{-1}{4}[/tex]
Step-by-step explanation:
A quadratic equation has one root if the discriminant is 0.
That is we need [tex]b^2-4ac=0[/tex] for this particular question.
Compare the following to find [tex]a,b, \text{ and } c[/tex]:
[tex]ax^2+bx+c=0[/tex]
[tex]my^2+2y-4=0[/tex]
The variable [tex]x[/tex] is representative of the variable [tex]y[/tex] here.
[tex]a=m[/tex]
[tex]b=2[/tex]
[tex]c=-4[/tex]
Plug in into [tex]b^2-4ac=0[/tex]:
[tex](2)^2-4(m)(-4)=0[/tex]
[tex]4+16m=0[/tex]
Subtract 4 on both sides:
[tex]16m=-4[/tex]
Divide both sides by 16:
[tex]m=\frac{-4}{16}[/tex]
Reduce:
[tex]m=\frac{-1}{4}[/tex]
The value of m for which the equation my² + 2y - 4= 0 has exactly one root is m = -1/4
How to find the roots of a quadratic equation?
Suppose that the given quadratic equation is
[tex]ax^2 + bx + c = 0[/tex]
Then its roots are given as:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
How to use discriminant to find the property of solutions of given quadratic equation?
Let the quadratic equation given be of the form [tex]ax^2 + bx + c = 0[/tex], then
The quantity [tex]b^2 - 4ac[/tex] is called its discriminant.
The solution contains the term [tex]\sqrt{b^2 - 4ac}[/tex] which will be:
- Real and distinct if the discriminant is positive
- Real and equal if the discriminant is 0
- Non-real and distinct roots if the discriminant is negative
There are two roots of a quadratic equations always(assuming existence of complex numbers). We say that the considered quadratic equation has 2 solution if roots are distinct, and have 1 solutions when both roots are same.
For this case, we've got the quadratic equation as:
[tex]my^2 + 2y - 4= 0[/tex]
Its discriminant would be:
[tex]D = 2^2 - 4(m)(-4) = 4 +16m[/tex]
For exactly one root, we need both roots to be same.
Thus, the discriminant would be 0.
Therefore, we get:
[tex]4 + 16m = 0\\m = \dfrac{-4}{16} = -\dfrac{1}{4}[/tex]
Real roots of a quadratic equation refers to the points where they intersect the axis of the variable they hold. Its plot is given below.
Thus, the value of m for which the equation my² + 2y - 4= 0 has exactly one root is m = -1/4
Learn more about discriminant of a quadratic equation here:
https://brainly.com/question/18659539
