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Mathematics
Graham Moran
13 July, 23:12
Potential roots of p (x) = x^4 - 9x^2 - 4x + 12
+1
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1
)
Moriah Vargas
14 July, 00:38
0
-6, - 4, - 3, - 2, - 1, 1, 2, 3, 4, 6
Step-by-step explanation:
The general formula for a fourth-degree polynomial is
f (x) = ax⁴ + bx³ + cx² + dx + e
Your polynomial is
f (x) = x⁴ - 9x² - 4x + 12
a = 1; e = 12
According to the Rational Roots Theorem, the possible rational roots are the factors of e divided by the factors of a.
Factors of e = ±1, ±2, ±3, ±4, ±6
Factors of a = ±1
Potential roots are x = ±1 ±2, ±3, ±4 ± 6
Putting them in order, we get the potential roots
x = - 6, - 4, - 3, - 2, - 1, 1, 2, 3, 4, 6
(The graph of your function shows roots at x = - 2, x = 1, and x = 3.)
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