What does the discriminant really tell us? Alevel maths

I thought the discriminant just told us if a curve intersects with the x axis once twice or never.
I never knew the discriminant really tells us how many solutions there are?

Reply 1

mqb2766

Original post by harlz_chalamet

I thought the discriminant just told us if a curve intersects with the x axis once twice or never.
I never knew the discriminant really tells us how many solutions there are?

If a solution corresponds to intersecting the x-axis (it usually does), then those two things youve said are the same thing as a solution corresponds to a root.

Reply 2

C_H_B

It’s kind of the same thing. You have a quadratic equation, which corresponds to a graph on a set of axes. The equation is set equal to zero, meaning that the output is zero, and you want to find the values of x for which the output (aka ‘y value’) is zero. So, the solutions you get are equal to the x values, when y=0. This is the same as the x axis intersects. We have established that solutions = intersects. The discriminant tells you how many times the x axis is crossed, and this is the same as telling you how many solutions there are (how many x values for which y=0).

Reply 3

souptf

In the quadratic formula, the discriminant is the part you add and subtract to -b before dividing by 2a. Depending on how many solutions the square root has you will get either one, two or no separate real values.