Roots — Algebra I · Grade 9 or accelerated Grade 8, what it means and where it is taught
The x values where y = 0.
Taught in Algebra I · Grade 9 or accelerated Grade 8.
Where it is taught
What uses it later
This idea is needed for:
- Degree — The highest power of x. It caps the number of roots and the number of turns.
Practise this idea
16 questions in the course bank use Roots, in Squares & Square Roots, Graphing Quadratics, Solving Quadratic Equations, Dividing Polynomials & the Factor Theorem, Polynomial Functions & Their Graphs, Complex Numbers. The first 8 are below; the rest are in those units.
Problem 1
Compute √144 + √25.
Worked answer
17
12 + 5 = 17
Note this is NOT √169 = 13 — roots do not add that way.
Problem 2
Which is larger, √16 + 9 or √16 + √9?
- √16 + 9
- √16 + √9
- They are equal
Worked answer
√16 + √9
√16 + 9 = √25 = 5
√16 + √9 = 4 + 3 = 7
7 > 5, so √a+b ≠ √a + √b.
Problem 3
Find the roots of y = x2 - 5x + 6.
Worked answer
2 and 3
(x-2)(x-3) = 0
x = 2 or x = 3
Problem 4
The roots of a parabola are -1 and 7. Find the axis of symmetry.
Worked answer
x = 3
-1 + 72 = 3
x = 3
Problem 5
Find the roots of y = 2x2 - 8x.
Worked answer
0 and 4
2x(x - 4) = 0
x = 0 or x = 4
Never divide by x — it would lose the root 0
Problem 6
Solve (x - 2)2 = 25.
Worked answer
7 and -3
x - 2 = ± 5
x = 7 or x = -3
Problem 7
Factor x3-7x+6 completely. Give the three roots, smallest first, separated by commas.
Worked answer
-3,1,2
f(1)=1-7+6=0
Dividing gives x2+x-6=(x+3)(x-2)
Roots -3, 1, 2
Problem 8
Which list contains every possible rational root of x3-2x2+x-6?
- ±1,±2,±3,±6
- ±1,±2
- ±1,±6
- ±2,±3
Worked answer
±1,±2,±3,±6
The constant is -6
Its divisors are 1, 2, 3, 6, positive and negative