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poizon [28]
1 year ago
9

Find a degree 3 polynomial having zeros -5, 1 and 5 and the coefficient of x^3 equal 1

Mathematics
1 answer:
mote1985 [20]1 year ago
7 0

Answer:

x^3 -x^2 -25x +25

Step-by-step explanation:

\text{The roots are,}~ \alpha  = -5,~ \beta = 1 ~ \text{and}~ \gamma = 5\\\\\text{The polynomial is,}\\\\~~~x^3 - (\alpha + \beta + \gamma)x^2+(\alpha \beta + \beta \gamma+ \gamma \alpha)x - \alpha\beta \gamma\\\\=x^3 - (-5+1+5)x^2 +(-5 \cdot 1 + 1 \cdot 5 + 5 \cdot -5)x - (-5)(1)(5)\\\\=x^3 -(0+1)x^2 + (-5+5-25)x +25\\\\=x^3 -x^2 -25x +25

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The distributive property is 15+45 = (10 + 40) + (5+5) = 50 + 10 = 60 Hope this helps you.
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Find the tangent line approximation for 10+x−−−−−√ near x=0. Do not approximate any of the values in your formula when entering
Svetllana [295]

Answer:

L(x)=\sqrt{10}+\frac{\sqrt{10}}{20}x

Step-by-step explanation:

We are asked to find the tangent line approximation for f(x)=\sqrt{10+x} near x=0.

We will use linear approximation formula for a tangent line L(x) of a function f(x) at x=a to solve our given problem.

L(x)=f(a)+f'(a)(x-a)

Let us find value of function at x=0 as:

f(0)=\sqrt{10+x}=\sqrt{10+0}=\sqrt{10}

Now, we will find derivative of given function as:

f(x)=\sqrt{10+x}=(10+x)^{\frac{1}{2}}

f'(x)=\frac{d}{dx}((10+x)^{\frac{1}{2}})\cdot \frac{d}{dx}(10+x)

f'(x)=\frac{1}{2}(10+x)^{-\frac{1}{2}}\cdot 1

f'(x)=\frac{1}{2\sqrt{10+x}}

Let us find derivative at x=0

f'(0)=\frac{1}{2\sqrt{10+0}}=\frac{1}{2\sqrt{10}}

Upon substituting our given values in linear approximation formula, we will get:

L(x)=\sqrt{10}+\frac{1}{2\sqrt{10}}(x-0)  

L(x)=\sqrt{10}+\frac{1}{2\sqrt{10}}x-0

L(x)=\sqrt{10}+\frac{\sqrt{10}}{20}x

Therefore, our required tangent line for approximation would be L(x)=\sqrt{10}+\frac{\sqrt{10}}{20}x.

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2 years ago
Which ordered pair is the solution to the system of equations? {y=x−4−4x+3y=−3 (−9, −13)
Leviafan [203]
The correct answer is (-9, -13)

p.s I already took the test and this was right
hope I helped :)
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3 years ago
Go on this one https://brainly.com/question/21200034<br><br> But other than that stay here.
Flura [38]

Answer:

ok thank you so much your the best

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3 years ago
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