Find all the zeros of the equation.
x^4 - 6x^2 - 7x - 6 = 0
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Using Descartes rule of signs, there is one positive root, one or three negative roots.
I'm sorry, I'm so confused. I don't really know what I am suppose to do or use to figure this problem out
The factorization theorem says if there are rational roots, they would be the factors of 6, or you can try factors like (x+1), (x-1), (x-2), (x+2), (x-3),(x+3),(x-6),(x+6).
Since it can be shown that x+1 and x-1 are not factors, there are two out of the remaining six are zeroes.
Let f(x)=x^4 - 6x^2 - 7x - 6 , you can try
But since f(-2)=16-24+14-6=0, we conclude that x=-2 is a zero.
Continue trying f(3) [because -2*3=-6, the constant term to see if x=3 is a zero.
Not the answer you are looking for? Search for more explanations.
Oh I get it. So I am just plugging in numbers 1 - 6 both positive and negative to see which one(s) will equal zero, correct ?
Yes, except that you only plug in factors of 6. So you can skip 4 and 5, because 4 and 5 are not factors of 6. This is true when the leading coefficient is 1 (i.e. 1x^4).
If the leading coefficient is not 1, then we have to check all combinations of
(ax\(\pm b)\), where a is one of the factors of the leading coefficient, and b is one of the factors of the constant term.
Thank you for the medal.