Ask question

Ask question

All categories

1 year ago

9

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

1 answer:

mote1985 [20]1 year ago

7 0

Answer:

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

Step-by-step explanation:

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

You might be interested in

What is the distributive property of 15+45

Taya2010 [7]

The distributive property is 15+45 = (10 + 40) + (5+5) = 50 + 10 = 60 Hope this helps you.

5 0

3 years ago

Tony spent $11.52 for some pens that were on sale for $.72 each how many pens did Tony bye

Semenov [28]

He will bye 16 pens hope that helps u

6 0

3 years ago

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

8 0

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 :)

8 0

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

3 0

3 years ago