All categories

3 years ago

Write the standard form of the simplest polynomial with the roots 2, 3, and -3

1 answer:

5 0

$\text{If}\ x_1,\ x_2\ \text{and}\ x_3\ \text{are roots of a polynomial, then we can write that polynomial}\\\text{in form}\ (x-x_1)(x-x_2)(x-x_3).\\\\\text{We have\ the\ roots:}\ 2,\ 3\ \text{and}\ -3.\\\\w(x)=(x-2)(x-3)(x-(-3))=(x-2)\underbrace{(x-3)(x+3)}_{use\ a^2-b^2=(a-b)(a+b)}\\\\=(x-2)(x^2-9^2)=(x-2)(x^2-9)=(x)(x^2)+(x)(-9)+(-2)(x^2)+(-2)(-9)\\\\=x^3-9x-2x^2+18=\boxed{x^3-2x^2-9x+18}$

You might be interested in

Which of the following is not equal to sin⁡(-230°)?

xenn [34]

From trigonometry we know that:

if $sin(\theta)=sin(\alpha)$

then, $\theta=n\pi+(-1)^n\alpha$ (where $n$ is an integer)

This can be rewritten in degrees as:

$\theta=n(180^{\circ})+(-1)^n\alpha$ .............(Equation 1)

Now, in our case, $\alpha=-230^{\circ}$

Therefore, (Equation 1) can be written as:

$\theta=n(180^{\circ})+(-1)^n(-230^{\circ})$ ..........(Equation 2)

Now, to find the correct options all that we have to do is replace n by relevant integers and find the values of $\theta$ that match.

For n=2, (Equation 2) gives us: $\theta=2\times 180^{\circ}+(-1)^2(-230^{\circ})=360^{\circ}-230^{\circ}=130^{\circ}$ .

Thus, $sin(230^{\circ})=sin(130^{\circ})$

Now, we know that: $-sin(-50^{\circ})=sin(50^{\circ})$

Let n=-1, then:

$\theta=(-1)\times 180^{\circ}+(-1)^{-1}(-230^{\circ})=-180^{\circ}+230^{\circ}=50^{\circ}$

Thus, $sin(-230^{\circ})=-sin(-50^{\circ})$

Likewise, $sin(-230^{\circ})=sin(50^{\circ})$

Only the last option $sin(-50^{\circ})$ will never match $sin(-230^{\circ})$ because no integral value of $n$ will ever give $\theta=-50^{\circ}$

Thus the last option is the correct option.

3 0

2 years ago

Read 2 more answers

HELP PLEASE Find the equation of the line<br> The line passes through the points (2, 3) and (-3, -2)

Vladimir79 [104]

Y= x+1

y-3 = (-2-3)/(-3-2) (x-2)
y-3 = 1 (x-2)
y = x-2+3
y=x+1

Mark brainliest please

7 0

2 years ago

Mistaken giving brainliest!!! Tho

vitfil [10]

Answer:

its C

Step-by-step explanation:

;););)

8 0

2 years ago

Read 2 more answers

Charlotte borrows $9000 to buy a second-hand car. The loan must be repaid

QveST [7]

Answer:

$13,400

Step-by-step explanation:

Simple Interest = principal × rate × time

principal= $9000

Rate= 12/100=0•12

Time=5years

Simple interest =PRT

= 9000× 0•12 × 5

= 5400

Total amount to be paid = 9000 + 5400

= $13400

8 0

3 years ago

HELP NOW!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11 Water boils at 212 degrees __________ A. Ce

34kurt

<span>alright it would have been easier if u took a pic but i think its a matching prob with choices A thro F:

Water boils at 212 degrees __________

A. Celsius Incorrect

Water boils at 100 degrees _________

B. Kelvin Incorrect

Water boils at 373 _______

C. Thermal Equilibrium Incorrect

Temperature at which all kinetic energy stops

D. Thermal Energy Incorrect

Reached when 2 objects have the same temperature

E. Absolute zero Incorrect

Sum of all kinetic energy and potential energy in an object's particles

F. Fahrenheit

So here are the correct matches:

</span>Water boils at 212 degrees __________F. Fahrenheit

Water boils at 100 degrees _________ A. Celsius

Water boils at 373 _______ B. Kelvin

Temperature at which all kinetic energy stops______E. Absolute zero

Reached when 2 objects have the same temperature ________C. Thermal Equilibrium

Sum of all kinetic energy and potential energy in an object's particles _____ D. Thermal Energy

7 0

3 years ago