Question

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

Answer 1

4. two real solutions

Explanation:

`x^2 - x = 1` (Given)

`\implies x^2-x-1=0`

• Equating it with
  `ax^2+bx+c=0`
• 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
  `\implies b^2-4ac`

`b^2-4ac\\=(-1)^2-4(1)(-1)\\=1+1=2>0\\\implies b^2-4ac >0`

-> Given quadratic equation has two real solutions.