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

Answer:

1001

1

Step-by-step 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.