Use the discriminant to determine how many and what kind of solutions the quadratic equation x^2 - x = 1 has.


1. no real or complex solutions

2. two complex (nonreal) solutions

3. one real solution

4. two real solutions

Respuesta :

Answer:

4. two real solutions

Step-by-step explanation:

[tex]x^2 - x = 1[/tex] (Given)

[tex]\implies x^2-x-1=0[/tex]

  • Equating it with [tex]ax^2+bx+c=0[/tex]
  • We find: a = 1, b = -1, c = -1
  • Next, we calculate the discriminant of the given quadratic equation by plugging the values of a, b and c in the formula [tex]\implies b^2-4ac[/tex]

[tex]b^2-4ac\\=(-1)^2-4(1)(-1)\\=1+1=2>0\\\implies b^2-4ac >0[/tex]

-> Given quadratic equation has two real solutions.

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