Question

Question #c8554

Answer 1

The discriminant is `-31`, meaning there are `2` complex solutions.

Explanation:

The discriminant is found in the quadratic formula:

`(-b+-sqrt(b^2-4ac))/(2a)`

with the discriminant being

`b^2-4ac`

Let's call the discriminant `d`:

`d<0->"two zeroes that are complex numbers"`

`d=0->"one real zero or a repeated zero"`

`d>0->"two distinct real zeroes"`

We have the equation `x^2-3x+10` already in `ax^2+bx+c` standard form, so plug into the formula:

`(-3)^2-4*1*10`

`9-40=-31`

`d=-31`

The discriminant is `-31`, meaning there are `2` complex solutions.

Bonus: Finding the complex solutions

Plug into the quadratic formula:

`(-(-3)+-sqrt((-3)^2-4*1*10))/(2*1)`

`(3+-sqrt(-31))/2`

Assume `sqrt(-1)` is `i`

`(3+-sqrt(31*-1))/2`

`(3+-sqrt(31)i)/2`

The zeroes are

`(3+sqrt(31)i)/2`, and `(3-sqrt(31)i)/2`

Here is a graph for reference: graph{x^2-3x+10 [-31.76, 32.96, -1.82, 30.53]}

Have a nice day!

Answer 2

The discriminant is `-31`.

Explanation:

To find the discriminant, you have to use the quadratic formula:

`color(white)=x=(-b+-sqrt(b^2-4ac))/(2a)`

The discriminant part is `b^2-4ac`. We need to identify the `a`, `b`, and `c` in our quadratic:

`color(white)=x^2-3x+10`

`a` is 1, `b` is `-3`, and `c` is `10`. Now plug these into the discriminant:

`color(white)(=>)b^2-4ac`

`=>(-3)^2-4(1)(10)`

`=9-40`

`=-31`

The discriminant is `-31`, which means that the quadratic has no real roots.