Question

Use the equation: 10x3 + 9x2 – 19x + 6

The total number of roots would be:


Select one:


a. 0

b. 1

c. 2

d. 3

Answer 1

@ShadowLegendX @v

Answer 2

@ganeshie8

Answer 3

1) It's not an equation.
2) If f(x) = 10x3 + 9x2 – 19x + 6

Find the number of sign changes in f(x) and f(-x) and answer the question.

Answer 4

I got 0 am I correct

Answer 5

Zero what?

Let's see, f(x) = 10x3 + 9x2 – 19x + 6. That's ++-+. I count two sign changes. So, there could be 2 or 0 Positive Real Roots.

f(-x) = -10x3 + 9x2 + 19x + 6. That's -+++. I count one sign change. So, there must be 1 Negative Real Root.

See how that works?

Answer 6

so the answer is 1

Answer 7

There MUST be 1. There MIGHT be 3.

Answer 8

so which do I pick then

Answer 9

Well, you have to prove it. The next particularly useful idea is the Rational Root Theorem. Do you know it?

Answer 10

no I don't.. why do you make this problem hard

Answer 11

this is like a 2 minute question not a 30 minute question we are getting nowhere

Answer 12

Try to remember that you wrote the problem statement from the assignment you were given. I'm just trying to help YOU solve it. This is how one proceeds. We are not learning a process consisting of playing with symbols. We are learning how to think linearly. This is a new language for some. I get that.

You should know the Rational Root Theorem. When you get a chance, ask about it -- or look it up. It's important.

For now, knowing the Rational Root Theorem, we are almost immediately in luck with x = -2. This gives f(x) = 10x3 + 9x2 -19x + 6 = (x+2)(10x^2 - 11x + 3). We managed to factor it to a linear factor and a quadratic factor. This is progress.

Okay, we found the Negative Real Root. How do you propose we find out if there are any Positive Real Roots?

Answer 13

For the record, you are right on one point, that this problem would take me about 30 seconds. That's only because I am used to the thinking process that is required. You may need to get accustomed to the thinking process. Be patient with yourself.

You are not correct that we are getting nowhere. We are gaining information about the particular problem and we are training our brains to think it a way that WILL result in a solution. There are lots of ways to think, but only some of them have a guarantee like that.

Answer 14

so I should pick answer B?

Answer 15

Either B or D.

You didn't answer my question.

How do you propose we find out if there are any Positive Real Roots?

Solve: 10x^2 - 11x + 3 = 0, maybe?