Solving Equations with Roots
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Objective
I can solve a 4th degree equation given it's roots
Part 1 of 4
Warm-up video
Mr. S Math · 5:54
We don't generate video — this one is by Mr. S Math on YouTube. The practice questions and exit ticket below were drafted by AI for this objective, and every question is editable in the teacher guide.
Part 2 of 4
Key concepts
3 concepts
- 1
According to the fundamental theorem of algebra, a fourth degree equation will have four solutions, also known as roots.
- 2
Synthetic division can be used to divide the original polynomial by the given roots to simplify the equation and find the remaining roots.
- 3
The quadratic formula, x = (-b ± √(b² - 4ac)) / 2a, is used to solve for the roots of a quadratic equation that cannot be factored, potentially resulting in imaginary solutions.
Part 3 of 4
Practice
10 questions
The degree of the polynomial equation x⁴ - 2x³ + x² - 4 = 0 is ____.
According to the Fundamental Theorem of Algebra, the equation x⁴ - 2x³ + x² - 4 = 0 has _______ solutions (roots).
Part 4 of 4
Exit ticket
Quick comprehension check
“Solve for all roots of the equation x⁴ - x³ - x² + x = 0, given that x = 1 and x = -1 are roots.”
Sample answer included in the free materials
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