anonymous
  • anonymous
What is the sum of the roots of a polynomial shown below f(x)=3x^3+12x^2+3x-18
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
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.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Let a, b, and c be the roots of this polynomial. Then the sum of the roots would be a+b+c. If we were to factor the polynomial, we would get \[f(x)=3x^3+12x^2+3x-18=3(x-a)(x-b)(x-c)\] Note however that if you were to expand the right hand side, you would get \[3(x-a)(x-b)(x-c)=3(x^3-(a+b+c)x^2+ \cdots)=3x^3-3(a+b+c)x^2 + \cdots\] Thus, you have both \[f(x)=3x^3+12x^2+\cdots=3x^3-3(a+b+c)x^2+\cdots\] Thus, by equating the coefficients of the x^2 term, you have \[12=-3(a+b+c) \implies a+b+c=-4\] Thus, the sum of the roots is -4 (even though you don't even know what the roots are!!!).

Looking for something else?

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