Respuesta :
Using the discriminant to know about the nature of the solution of the quadratic equation x² -x = -1/4 tells us the fact as given by: Option c. one real solution
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, the given equation is:
[tex]x^2 - x = -1/4[/tex]
Converting this to the form [tex]ax^2 + bx + c = 0[/tex], we get:
[tex]x^2 - x + 1/4= 0\\or\\4x^2 -4x + 1 = 0[/tex]
Thus, we get:
a = 4, b = -4, c = 1
Putting these values in the expression for discriminant, we get:
[tex]D = b^2 - 4ac =(-4)^2 - 4(4)(1) = 16 - 16 = 0[/tex]
The discriminant is 0, so the considered quadratic equation is going to have both roots real and equal. Or in terms of distinct solutions, it is going to have one real solution (distinct).
Thus, using the discriminant to know about the nature of the solution of the quadratic equation x² -x = -1/4 tells us the fact as given by: Option c. one real solution
Learn more about discriminant of a quadratic equation here:
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