11th grade Find all the roots: the Rational Root Theorem, conjugate pairs and Descartes' Rule of Signs worksheet

Find all the roots: the Rational Root Theorem, conjugate pairs and Descartes' Rule of Signs

Grade 11 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Esme's robot finds one rational root of x³ + 3x² + 4x + 12. What are all its roots?
2. 2.

   Jun finds that 3x³ + 2x² + 3x + 2 has one rational root. What are all its roots?
3. 3.

   Kira finds one rational root of x³ − 4x² + 25x − 100. What are all its roots?
4. 4.

   Milo's robot needs a degree 3 polynomial with real coefficients, leading coefficient 1, and roots -1 and 2 − i. What is it in standard form?
5. 5.

   Noah needs a degree 3 polynomial with real coefficients, leading coefficient 1, and roots 3 and -2 + i. What is it in standard form?
6. 6.

   Ren needs a degree 3 polynomial with real coefficients, leading coefficient 1, and roots -4 and 1 + 2i. What is it in standard form?
7. 7.

   Tala's polynomial has degree 6 and real coefficients. Two roots are 7i and 3 + 8i; every other root is real. How many real roots does it have, counting repeats?
8. 8.

   Zee's robot has a degree 7 polynomial with real coefficients. Two roots are 6i and 4 − 8i; the rest are real. How many real roots, counting repeats?
9. 9.

   Bo has a degree 5 polynomial with real coefficients. One root is 9i, and every other root is real. How many real roots does it have, counting repeats?
10. 10.

    Esme has a degree 10 polynomial with real coefficients. Two roots are 4i and 9 + 2i; the rest are real. How many real roots, counting repeats?