Question

Find the value of the discriminant and describe the number and type of roots.

6x2 -x - 12 = 0

Answer 1

You know the quadratic formula? This thing:
\[\Large \frac{-b \pm \sqrt{b^2-4ac}}{2a}\]

The discriminant is the part of that equation that is under the square root.
b^2-4ac

Why is that part of the equation so important that it has its own name? Because it tells us what kinds of solutions the equation will have.
If we do b^2-4ac and the result is negative, then when we try to take the square root of that negative number, we'll get an imaginary number, so both of our answers will be complex.
If we do b^2-4ac and the result is 0, then it basically drops out entirely, and our answer will just be -b/2a, so there's just 1 root.
If we do b^2-4ac and the result is positive, then there will be 2 roots. If the result is something that can be square rooted simply, like 4, 9, 16, 25, etc... then the roots will be rational. If the result can't be square rooted easily, then we end up with 2 real but irrational roots.

Answer 2

To summarize:
The discriminant is b^2-4ac.
If the discriminant is:
negative, then you have 2 complex roots.
0, then you have 1 real, rational root.
Positive and square-root-able, then you have 2 real rationals roots.
Positive and not square-root-able, then you have 2 real and irrational roots.

Answer 3

see im confused on the b wat is the b?

Answer 4

The a, the b, and the c come from your equation.
ax^2 + bx +c

So if I have the equation
5x^2 -4x +1 =0
then a=5 b=-4 and c=1

If I have the equation
x^2 -10x -50 =0
then a=1 b=-10 and c=-50

If I have the equation
-3x^2 +x -16 = 0
then a = -3 b=1 and c = -16

If I have the equation
5x^2 +1 = 0
then a = 5 b=0 and c=1

Understand?

Answer 5

ohhh ohk

Answer 6

So, look at your problem and tell me what a, b, and c are.

Answer 7

a=6 b=-1 and c=-12

Answer 8

Cool =) So what is the discriminant?