• anonymous
Find the real and complex zeros of the following function. f(x)=x^3-6x^2+21x-26
  • Stacey Warren - Expert
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.
  • schrodinger
I got my questions answered at in under 10 minutes. Go to now for free help!
  • Rogue
Some possible roots for this function are\[\pm 1, \pm 2, \pm 13, \pm 26\]since those are the possible factors of the constant, 26, divided by the possible factors of the leading coefficient, 1. Using synthetic division, you can test those out to see which ( x- a) is a factor. You'll see that 2 works. So now the polynomial gets factored into:\[f(x) = (x-2)(x^2 - 4x +13)\] Inspecting the quadratic will tell you that it is irreducible, you can have to solve it via the quadratic formula. Do so and you will see that your three solutions are:\[x =2, x = 2 \pm 3i\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.