Question

help!!!!!:(
Use the discriminant to describe the roots of each equation. Then select the best description.

x2 - 5x - 4 = 0


double root
real and rational root
real and irrational root
imaginary root

Answer 1

i will gave medals.....just help me.....

Answer 2

Know what the discriminant is?

Answer 3

on...i don't know were i should start...

Answer 4

Some nasty lag today... in the quadratic formula, the part under the square root is the discriminant:

\(\dfrac{-b\pm \sqrt{\color{red}{b^2-4ac}}}{2a}\)

Answer 5

If \(b^2-4ac=0\) then there is only one root. If it is negative, well, then it is a pair of complex/imaginary roots. The rational/irrational part depends on if it could come out from under the root sign.

Answer 6

So in \(x^2 - 5x - 4\) you have \(a=1\), \(b=-5\), and \(c=-4\), so put them into the \(b^2-4ac=?\) and see what you get.

Answer 7

-9

Answer 8

Remember, the \(b^2\) means negatives become postitives. \(b^2=(-5)^2=(-5)(-5)=25\)

Answer 9

o i see......which one of the choices will it be???

Answer 10

Well, lets work with that 25.

\(b^2-4ac\implies \)
\((-5)^2-4(1)(-4)\implies \)
\(25+16\implies \)
\(b^2-4ac=41\)

Now, this is what would be under the root. So does \(\sqrt{41}\) have a nice, simple root or is it irrational? It is positive, so it will not be complex. But is it rational or irrational?

Answer 11

rational....

Answer 12

So you can get 41 out of the root? What is \(\sqrt{41}\)? I mean, \(\sqrt{64}=8\), if you do that to \(\sqrt{41}\), what do you get? Not sure? Put it in a calculator.

Answer 13

i got 6.4...

Answer 14

And a bunch of other decimals. 6.40312423743... So it is not rational.

Answer 15

then what is i?????? i hate that stuff..i just don't get it...

Answer 16

So far it has been proven to be not rational, and not complex/imaginary.

Do you know what non imaginary means? Two of these have been eliminated:

double root
real and rational root
real and irrational root
imaginary root

Answer 17

when the answer is negative...right???

Answer 18

Imaginary is when it is negative.

What I was trying to get at is this: The opposite of imaginary is real. So it IS real, and it IS irrational. It is NOT imaginary and it is NOT rational. So the only question left is what is a double root?

Well, I looked that up for you:
What Is a Double Root in Algebra?
Answer
A double root is a fact in algebra where a trinomial is factored and the resulting roots are equal. The individual roots can then be equalled with a number like zero and therefore they are referred to as double roots. Also, a double root of a quadratic equation is always rational because a double root can occur when the radical disappears.

So, that eliminates one more, leaving only the answer.

Answer 19

real and irrational root ...right????

Answer 20

Yes. Because they are not the same root, it is not double, and that is all that would be left a that point.

Answer 21

ok thank alot.....

Answer 22

That is how you can answer a lot of these. Eliminate impossibilities. If the discriminant is 0, it is double. Otherwise it is NOT double. If it is - then it is complex/imaginary, otherwise it is real. If it able to come out of the root nicely it is rational, otherwise it is irrational. Each one eliminates some things or confirms some.

Answer 23

k..thank again...u really helped...i only have anther 15 to do....lol

Answer 24

Well, hopefully with knowing how it works you can do them more quickly!

Answer 25

i will have to go over ur examples again....but i think i will be able to do them...soooo