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3 years ago

If using the method of completing the square to solve the quadratic equation

Mathematics

1 answer:

jenyasd209 [6]3 years ago

4 0

You add half of the coefficient of x and square it.

What you do on one side,you must do it on the other.

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<img src="https://tex.z-dn.net/?f=15%20%2B%2015%20%2B%2030" id="TexFormula1" title="15 + 15 + 30" alt="15 + 15 + 30" align="absm

gogolik [260]

15+15+30=(15+15) +30=30+30=60
your number is 60

8 0

3 years ago

Find an nth-degree polynomial function with real coefficients satisfying the given conditions.

lesya692 [45]

Answer:

$\displaystyle f(x) = -2(x-2)(x^2+4)$

Step-by-step explanation:

We want to find a third degree polynomial with zeros x = 2 and x = 2i and f(-1) = 30.

First, note that by the Complex Root Theorem, since x = 2i is a root, x = -2i must also be a root.

Hence, we will have the three factors:

$\displaystyle f(x) = a(x-(2))(x-(2i))(x-(-2i))$

Where a is the leading coefficient.

Expand and simplify the second and third factors:

$\displaystyle \begin{aligned} (x-(2i))(x-(-2i)) &= (x-2i)(x+2i) \\ \\ &= x(x-2i)+2i(x-2i) \\ \\ &= (x^2 - 2ix) + (2ix - 4i^2) \\ \\ &=x^2 + 4\end{aligned}$

Hence:

$\displaystyle f(x) = a(x-2)(x^2+4)$

Since f(-1) = 30:

$\displaystyle \begin{aligned} f(x) &= a(x-2)(x^2+4) \\ \\ (30) &= a((-1)-2)((-1)^2+4) \\ \\ 30 &= -15a \\ \\ a&= -2\end{aligned}$

In conclusion, third degree polynomial function is:

$\displaystyle f(x) = -2(x-2)(x^2+4)$

5 0

3 years ago

Write a division story for 36/9

nalin [4]

Jerry had 36 goldfish and 9 friends he dived the gold fish evenly between his 9 friends

7 0

3 years ago

Nine buses hold 85 people each. If 693 people buy tickets for a trip, how many seats won’t be taken?

Greeley [361]

Answer:

Step-by-step explanation:

you take 85 * 9

85 = # of seats

9 = # of buses

then you get 765

next, you take 765 - 693

765 = # of seats

693 = # people who bought tickets for a trip

finally you get 72

72 = # of empty seats

4 0

3 years ago

Whats the reciprocal of 4 3/7

Angelina_Jolie [31]

Answer

0.22580645161

Step-by-step explanation:

you just have to do 4 3/7 in a calculator

6 0

3 years ago