If a polynomial function f(x) has roots 0, 4, and 3+ the square root of 11, what must also be a root of f(x)
2 answers:
Answer: (3 - √11) is also a root of the polynomial f(x).
Step-by-step explanation: Given that a polynomial function f(x) has the following roots :
We are to find the value that must also be a root of f(x).
We know that
the irrational roots of a polynomial function always occur n pairs.
That is,
(a + b√c) is a root of a polynomial P(x), then its conjugate (a - b√c) will also be a root of P(x).
Given that
(3 + √11) is a root of the polynomial f(x), so we must have
the conjugate (3 - √11) is also a root of the polynomial f(x).
Thus, (3 - √11) is also a root of the polynomial f(x).
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Answer: C. At the α=0.05 significance level, they should conclude that more than 50% of adults support the tax increase.
Step-by-step explanation:
Given: Null hypothesis:
Alternative hypothesis:
p-value = 0.033
If the p-value is greater than alpha (p > . 05), then we fail to reject the null hypothesis.
If α=0.01 , then p-value > α i.e. we fail to reject the null hypothesis.
Conclusion: Exactly 50% of adults support the tax increase.
If α=0.05 then p-value < α i.e. we reject the null hypothesis.
Conclusion: more than 50% of adults support the tax increase.
Thus, Correct option: C .