What are the roots of the polynomial equation x^4+x^3=4x^2+4x?
–2, –1, 0, 2
–2, 0, 1, 2
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!
you could write everything on one side and try to factor
x^4 + x^3 - 4x^2 - 4x = 0
take out the common factor x
x(x^3 + x^2 - 4x - 4) = 0
so what is one root?
when two expression are multiplied and the result is zero then either one = zero
Not the answer you are looking for? Search for more explanations.
yes, so it would be D?
dont jump to conclusions
all we can say is that x = 0
one root is 0
- so it could be any of the 4 options
now we can look to see if we can factor the cubic in the parentheses
x^3 + x^2 - 4x - 4 = 0
we can factor this by grouping
can you factor the first 2 terms x ^3 and x^2
- what is the highest common factor of these 2?
what is the highest thing which divides into x^3 and x^2?
is it x or is it x^2?
it would be x^2
so it factors to x^2(x + 1)
OK with that?
right so so far we have
x^1(x + 1) - 4x - 4 = 0
it would be nice if we could get another (x + 1) so we could factor further and we can do this by taking out -4 from the lat 2 terms
so we get
x^2( x + 1) - 4(x + 1) = 0
taking out the x+ 1
(x^2 - 4)(x + 1) = 0
do you follow that ok?
sure do :)
great so now we have
x^2 - 4 = 0 and x + 1 = 0
x = 2 , -2 and -1
so final answer is
2, -2, -1 and 0
A is correct
Thank you for explaining this to me!!!
its always worth checking to see if you can factor by grouping