Question

Which of the following are possible discriminants for a quadratic function that crosses the x-axis twice? Check all that apply.

1001
1
-1
0

Answer 1

1001

1

Explanation:

If a quadratic function crosses the x-axis twice, it has two solutions. For a quadratic function in
`ax^2+bx+c` with discriminant
`b^2-4ac`, the following is true:

• If
  `b^2-4ac>0`, then the quadratic has two real solutions
• If
  `b^2-4ac=0`, then the quadratic has one real solution
• If
  `b^2-4ac<0`, then the quadratic has no real solutions

Therefore, in order to have two solutions, a quadratic's discriminant must be larger than 0. The only two answer choices that satisfy this are 1001 and 1.