Find all roots of P(x) = (x – 3)(x + 3)(x – 1).
Hint
x – 3 = 0, x + 3 = 0, or x – 1 = 0
Answer
The roots are 3, -3, and 1.
Write a polynomial with roots of -5, 5, and 1.
The factors are (x + 5), (x – 5), and (x – 1).
P(x) = x3 – x2 – 25x + 25
Or, P(x) = (x + 5)(x – 5)(x – 1)
Find all the roots of x3 + 6x2 – x – 6.
P(1) = (1)3 + 6(1)2 – (1) – 6 = 0
The roots are -6, -1, and 1.
Find all the roots of x3 – x2 – 49x + 49.
P(7) = (7)3 – (7)2 – 49(7) + 49 = 0
The roots are -7, 1, and 7.
Find all the roots of x3 – 8x2 – 4x + 32.
P(2) = (2)3 – 8(2)2 – 4(2) + 32 = 0
The roots are -2, 2, and 8.
Find all the roots of x3 + x2 – 100x – 100.
P(10) = (10)3 + (10)2 – 100(10) – 100 = 0
The roots are -10, -1, and 10.
Find all the roots of x4 – 13x2 + 36.
P(3) = (3)4 – 13(3)2 + 36 = 0
The roots are -3, -2, 2 and 3.
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