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?
Bo uses synthetic division on 2x³ − x² − 11x + 10 = 0. 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)?
- two real roots and no complex roots
- two real roots and two complex roots
- four real roots and no complex roots
- two real roots and one complex root
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 two complex roots
- two real roots and one complex root
- two real roots and no complex roots
- four real roots and no complex roots
Luz factors x⁴ + 13x² + 36 on graph paper. How many of its roots are real, and how many are complex (not real)?
- no roots at all
- four real roots and no complex roots
- no real roots and four complex roots
- no real roots and two complex roots
Milo factors x³ − 2x² + 9x − 18 by grouping. How many of its roots are real, and how many are complex (not real)?
- one real root and no complex roots
- one real root and two complex roots
- one real root and one complex root
- three real roots and no 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
- two or none
- three only
- 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, three, two, one or none
- three or one
- four, two or none
- four only
Tala uses Descartes' Rule of Signs on x³ + 2x² − 5x − 6. How many negative real roots can it have?
- two only
- one only
- two, one or none
- two or none