Find all the roots: the Rational Root Theorem, conjugate pairs and Descartes' Rule of Signs
Grade 11 Math Worksheet
Circle the best answer, or write your answer on the line.
Tala tests candidates for 2x³ − 3x² + 2x − 3 = 0 on a puzzle card. One root is a fraction. What is it?
Zee's robot tests candidates for 3x³ + 4x² − 13x + 6 = 0. One root is a fraction. What is it?
Esme tests candidates for 3x³ − 4x² + 6x − 8 = 0 in a notebook. One root is a fraction. What is it?
Jun factors x⁴ + 7x² − 18 for math club. How many of its roots are real, and how many are complex (not real)?
- four real roots and no complex roots
- two real roots and no complex roots
- two real roots and one complex root
- two real roots and two complex roots
Kira's robot factors x⁴ − 3x² − 4. How many of its roots are real, and how many are complex (not real)?
- two real roots and no complex roots
- four real roots and no complex roots
- two real roots and two complex roots
- two real roots and one complex root
Luz factors x⁴ + 13x² + 36 on graph paper. How many of its roots are real, and how many are complex (not real)?
- no real roots and two complex roots
- no roots at all
- no real roots and four complex roots
- four real roots and no complex roots
Milo factors x³ − 2x² + 9x − 18 by grouping. How many of its roots are real, and how many are complex (not real)?
- three real roots and no complex roots
- one real root and one complex root
- one real root and no complex roots
- one real root and two complex roots
Noah uses Descartes' Rule of Signs on x⁴ − 3x³ + 2x − 5. How many positive real roots can it have?
- three, two, one or none
- three only
- two or none
- three or one
Ren's robot uses Descartes' Rule of Signs on x⁵ − 2x⁴ − x³ + 4x² − 3x + 6. How many positive real roots can it have?
- four, two or none
- four only
- three or one
- four, three, two, one or none
Zee uses Descartes' Rule of Signs on 2x⁴ − x³ + 3x² + x − 4. How many negative real roots can it have?
- one or none
- three or one
- one only