Question

Can someone walk me through solving this? I know how to test positive and negative real zeros, I am just unsure of how to test fractions Which of the following represents the zeros of f(x) = 5x3 − 6x2 − 59x + 12?

4, 3, 1 over 5
4, 3, −1 over 5
4, −3, 1 over 5
4, −3, −1 over 5

Answer 1

You have several choices:

1) you could use synthetic division to determine whether 4 (for example) is a root of the given polynomial.
2) you could convert 4 (for example) into a factor (x-4) and determine whether (x-4) divides into the given polyn. with no remainder?

Answer 2

@Tennistar Can't you just convert the fractions into decimals, and then solve for the zeroes?

Answer 3

Its not so much the numbers 4 and 3 for example that trouble me, its the fractions. I am unsure of how to test those. I don't know if you can turn fractions into decimals and have it still work.

Answer 4

All the previous examples with which I learned from did not contain a fraction that needed to be tested to see if it was a zero.

Answer 5

And also, the challenge I am facing with this one is, all of the previous example "q" values were 1 or 2, and not something larger.

Answer 6

Turning fractions into decimals would likely make your work harder instead of easier.

Have you seen my suggestions, above?

Using synth div, you could check whether 1/5 is a root of the polynomial or not?

Or, starting with 1/5, form a possible factor and divide that factor into the given poly. Is there, or is there not, a remainder? The possible root 1/5 goes to form the possible factor (5x-1).

Answer 7

@mathmale Why would turning them into decimals make it harder?

Answer 8

Would you mind trying my suggestions? Then, if you're still interested, we could address that question.

Answer 9

So if I selected to use synthetic division, how would I do that using a fraction? Now what?