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Use the Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function:
f(x)= 5x^3+X^2X+5
 one year ago
 one year ago
Use the Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function: f(x)= 5x^3+X^2X+5
 one year ago
 one year ago

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mathmateBest ResponseYou've already chosen the best response.1
How many times did the expression changed sign?
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
There is then a MAXIMUM of 3 positive roots, but it could also be 1.
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
Now flip the sign of the coefficients of the odd powers. How many times does the new expression change sign?
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
The number of sign changes is the maximum number of positive roots, including complex. If there are two complex roots (as is the case), then there is only one (real) positive root.
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
so the negative right converted right?
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
Yes, the number of sign changes of the new expression (i.e. replace x by x) gives the MAXIMUM number of negative roots.
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
So for this one there is none for the negative and 1 for the positive
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
so how do you know there is one and not 3 for the positive?
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
Using the Descartes rule of signs, we do know that there is no negative root. But we do not know if there is ONE or THREE positive roots.
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
ok so the answer for positive is 1 and 3 and negative is 0
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
You can find that out by factoring the expression. A cubic has at least one real root, and we know that it is positive in this case.
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
Use the Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function: f(x)=3X^2+2X^2+x+3
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
how does this work then?
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
the positive looks like there is none and same with the negative?
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
Now, let's see. (1) The expression as is has no change in sign, so what do you conclude? (2) flip the sign of the odd powers to give 3X^3+2X^2x+3, sign changed 3 times, what do you conclude?
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
wait why is 3X^2 flipped?
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
I supposed you have a typo! It's 3x^3, ... or not?
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
Use the Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function: f(x)=3X^3+2X^2+x+3
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
ok so the positive is none then the negative is 3X^3+3X^2X+3, so 2 and 1
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
No positive is correct. Can you repeat the conclusion for negative?
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
of so negative is 3 and 1
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
The number of possible roots always differ by an even number because complex roots, if any, come in pairs. 1 and 2 will not be correct. 1 and 3 would be.
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
Perhaps more exactly, 1 OR 3.
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
ok thanks that makes sense
 one year ago
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