This is for question#30. You are right that the distance between A and D is 5, however what I marked in the figure is the distance from point D to the y-axis, which is 4 units. This would be the base of the resulting right triangle which has a height of 3 units. I hope this makes sense.

If you look at the graph of the function, the graph touches the x-axis at the origin, which corresponds to the root at $x=0$. And this means that the multiplicity of the root must be even at the origin, it can be 2, 4, etc. This means that we can eliminate choices A and E, where the multiplicity is odd in both the cases.

The general concept is that repeated roots are tied to a concept called multiplicity. The multiplicity of a root is the number of times a root is an answer. You can find the multiplicity of a root by looking at the exponent on the corresponding factor. If the multiplicity is even, the graph will touch the x-axis at that zero. That is, it will stay on the same side of the axis.

Sahil Kumar says

Shouldn’t the distance between A and D be 5?

Dabral says

Hi Sahil,

This is for question#30. You are right that the distance between A and D is 5, however what I marked in the figure is the distance from point D to the y-axis, which is 4 units. This would be the base of the resulting right triangle which has a height of 3 units. I hope this makes sense.

Dabral

Lucas Gerardo Gonzalez says

In Question 59. Exactly why are we eliminating answer choices A and E?

Dabral says

Hi Lucas,

If you look at the graph of the function, the graph touches the x-axis at the origin, which corresponds to the root at $x=0$. And this means that the multiplicity of the root must be even at the origin, it can be 2, 4, etc. This means that we can eliminate choices A and E, where the multiplicity is odd in both the cases.

The general concept is that repeated roots are tied to a concept called multiplicity. The multiplicity of a root is the number of times a root is an answer. You can find the multiplicity of a root by looking at the exponent on the corresponding factor. If the multiplicity is even, the graph will touch the x-axis at that zero. That is, it will stay on the same side of the axis.

Dabral