Potential roots of p(x) = x^4 - 9x^2 - 4x + 12
1 answer:
Answer:
-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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Answer:
31.82% probability that this day would be a winter day
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening
In this question:
Event A: Rain
Event B: Winter day
Probability of rain:
0.42 of 0.25(winter), 0.23 of 0.25(spring), 0.16 of 0.25(summer) or 0.51 of 0.25(fall).
So
Intersection:
Rain on a winter day, which is 0.42 of 0.25. So
If you were told that on a particular day it was raining in Vancouver, what would be the probability that this day would be a winter day?
31.82% probability that this day would be a winter day