Question

Use the discriminant to determine the nature of the roots of 4x2 + 15x + 10 = 0.

Answer 1

no it does not

Answer 2

The discriminant comes from the quadratic formula...the part that is under the radical sign. Here we use it without the radical sign, and our a is 4, our b is 15, and our c is 10. The discriminant is this:\[b ^{2}-4ac\]

Answer 3

Let's fill that in with our a, b, and c and see what we get for a value.

Answer 4

\[(15)^{2}-4(4)(10)\]\[225-160=65\]

Answer 5

Because the discriminant is positive (greater than 0), it will have 2 real solutions. The graph to this, generically speaking, would look something like this:

Answer 6

There are 2 real solutions shown where the graph intercepts the x axis twice. That's what "solutions" to an equation are...where the graph intercepts the x axis.

Answer 7

These are also called the zeros of your function.