Answer:
p = x² − 6x + 10
Step-by-step explanation:
Complex roots come in conjugate pairs. So if 3−i is a root, then 3+i is also a root.
p = (x − (3−i)) (x − (3+i))
p = x² − (3+i)x − (3−i)x + (3−i)(3+i)
p = x² − 3x − ix − 3x + ix + (9 − i²)
p = x² − 6x + 10
You can check your answer using the quadratic formula.
x = [ -b ± √(b² − 4ac) ] / 2a
x = [ 6 ± √(36 − 40) ] / 2
x = (6 ± 2i) / 2
x = 3 ± i
Let's simplify step-by-step.<span><span><span>23.6−<span>7.1a</span></span>−<span>4.2b</span></span>−<span>(<span><span>5.8b</span>−<span>9a</span></span>)</span></span>Distribute the Negative Sign:<span>=<span><span><span>23.6−<span>7.1a</span></span>−<span>4.2b</span></span>+<span><span>−1</span><span>(<span><span>5.8b</span>−<span>9a</span></span>)</span></span></span></span><span>=<span><span><span><span><span><span>23.6+</span>−<span>7.1a</span></span>+</span>−<span>4.2b</span></span>+<span><span>−1</span><span>(<span>5.8b</span>)</span></span></span>+<span><span>−1</span><span>(<span>−<span>9a</span></span>)</span></span></span></span><span>=<span><span><span><span><span><span><span>23.6+</span>−<span>7.1a</span></span>+</span>−<span>4.2b</span></span>+</span>−<span>5.8b</span></span>+<span>9a</span></span></span>Combine Like Terms:<span>=<span><span><span><span>23.6+<span>−<span>7.1a</span></span></span>+<span>−<span>4.2b</span></span></span>+<span>−<span>5.8b</span></span></span>+<span>9a</span></span></span><span>=<span><span><span>(<span><span>−<span>7.1a</span></span>+<span>9a</span></span>)</span>+<span>(<span><span>−<span>4.2b</span></span>+<span>−<span>5.8b</span></span></span>)</span></span>+<span>(23.6)</span></span></span><span>=<span><span><span>1.9a</span>+<span>−<span>10b</span></span></span>+<span>23.6</span></span></span>
Answer:
The fifth degree Taylor polynomial of g(x) is increasing around x=-1
Step-by-step explanation:
Yes, you can do the derivative of the fifth degree Taylor polynomial, but notice that its derivative evaluated at x =-1 will give zero for all its terms except for the one of first order, so the calculation becomes simple:

and when you do its derivative:
1) the constant term renders zero,
2) the following term (term of order 1, the linear term) renders:
since the derivative of (x+1) is one,
3) all other terms will keep at least one factor (x+1) in their derivative, and this evaluated at x = -1 will render zero
Therefore, the only term that would give you something different from zero once evaluated at x = -1 is the derivative of that linear term. and that only non-zero term is:
as per the information given. Therefore, the function has derivative larger than zero, then it is increasing in the vicinity of x = -1
We have that This equation simply state that P as a Function of A is equal to 0.97
From the question we are told that
P(A) = 0.97.
Generally
This equation simply state that P as a Function of A is equal to 0.97
i.e P is a Constant equation and A is a variable that changes P to 0.97
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