1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Virty [35]
3 years ago
5

Find the sum of the roots the following equation. The subject is quadratic equations with a maximum power of two (things like a(

x^3)^2 + b(x^3) + c = 0 also count as a power of two) so we have to find a way to turn this into a quadratic equation. Please help.
\left(2x\:^2-3x\right)^2+4\left(2x^2-3x\right)+3=0
Mathematics
2 answers:
Alexus [3.1K]3 years ago
8 0

\bf (2x^2-3x)^2+4(2x^2-3x)+3=0\qquad \boxed{a=2x^2-3x}\implies a^2+4a+3=0 \\\\\\ (a+3)(a+1)=0\implies a= \begin{cases} -3\\ -1 \end{cases}\qquad \stackrel{\textit{their sum}}{-3-1\implies -4}

anastassius [24]3 years ago
3 0

Answer:

3/2

Step-by-step explanation:

(2x² − 3x)² + 4 (2x² − 3x) + 3 = 0

We can simplify this using substitution.  Let's say that u = 2x² − 3x.

u² + 4u + 3 = 0

Factoring:

(u + 3)(u + 1) = 0

u = -3, u = -1

Therefore:

2x² − 3x = -3, 2x² − 3x = -1

2x² − 3x + 3 = 0, 2x² − 3x + 1 = 0

For a quadratic ax² + bx + c = 0, the sum of the roots is -b/a.  So in both cases, the sum is 3/2.

You might be interested in
write a function g whose graph represents a translation 2 units to the right followed by a horizontal stretch by a factor or 2 o
Alenkinab [10]
\bf f(x)=&{{  A}}({{  B}}x+{{  C}})+{{  D}}
\\ \quad \\
y=&{{  A}}({{  B}}x+{{  C}})+{{  D}}
\\ \quad \\
f(x)=&{{  A}}\sqrt{{{  B}}x+{{  C}}}+{{  D}}
\\ \quad \\
f(x)=&{{  A}}(\mathbb{R})^{{{  B}}x+{{  C}}}+{{  D}}
\\ \quad \\
f(x)=&{{  A}} sin\left({{ B }}x+{{  C}}  \right)+{{  D}}\\\\
f(x)=&{{  A}} \left|{{ B }}x+{{  C}}  \right|+{{  D}}
\\\\
--------------------\\\\

\bf \bullet \textit{ stretches or shrinks horizontally by  } {{  A}}\cdot {{  B}}\\\\
\bullet \textit{ flips it upside-down if }{{  A}}\textit{ is negative}\\
\left. \qquad   \right.  \textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if }{{  B}}\textit{ is negative}\\
\left. \qquad   \right.  \textit{reflection over the y-axis}

\bf \bullet \textit{ horizontal shift by }\frac{{{  C}}}{{{  B}}}\\
\left. \qquad  \right. if\ \frac{{{  C}}}{{{  B}}}\textit{ is negative, to the right}\\\\
\left. \qquad  \right.  if\ \frac{{{  C}}}{{{  B}}}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by }{{  D}}\\
\left. \qquad  \right. if\ {{  D}}\textit{ is negative, downwards}\\\\
\left. \qquad  \right. if\ {{  D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{  B}}}

with that template in mind, let's see,
 
\bf f(x)=|x| \implies \begin{array}{lllccll}
f(x)=&1|&1x&+0|&+0\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}

so, to shift it to the right by 2 units, simply set C = 2.
to stretch it by 2, set A = 1/2.

the smaller A is, the wider it opens, the larger it is, the more it shrinks.
5 0
3 years ago
Convert 7/66 to a decimal equivalent
wlad13 [49]

\frac{7}{66} = 0.10606

Step-by-step explanation:

\frac{7}{66}

Since we have only one digit in the numerator and the denominator has 2 digits, we have to 0 along with 7, so that it becomes 70, 1 time 66 is 66, 70 - 66 = 4 is the remainder, so the quotient is 0.1, then along with 4 we have to add one 0 , so it becomes 40 which is lesser than 66 so one more 0 is added and then it becomes 400, 6 times 66 is 396, 400 - 396 = 4 again the process going on. The quotient is 0.10606...

4 0
3 years ago
Help with this answer plsssssss
Masteriza [31]

Answer:

168

Step-by-step explanatio16n:

V = lw ·h/3

8 0
3 years ago
Read 2 more answers
What is the closest whole number approximation of √50?
mr_godi [17]

Answer:

7

Step-by-step explanation:

√50 is close to √49

49 is a perfect square, 50 is close to 49.

√49 = 7

√50 ≈ 7.071068

6 0
2 years ago
Read 2 more answers
Please Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Oduvanchick [21]

Answer:

26:26

Step-by-step explanation:

I hope I've helped :)

4 0
3 years ago
Other questions:
  • Allen bought 1,350 shares of stock for $12 per share. If he sold all his shares for $27,000, how much profit on each share did h
    10·2 answers
  • Petra booked a family holiday.
    6·2 answers
  • Help with geometry, right triangle congruence and missing side/angle
    8·1 answer
  • 5. SHOPPING Two stores are having a sale on T-shirts
    12·1 answer
  • Calculate the number of vertices in a full 5-ary tree with 35 internal vertices.
    9·1 answer
  • How much do you need to subtract from 31/6 to make<br> 5?
    14·2 answers
  • If a factor of a polynomial p(x)=2​
    9·1 answer
  • Which of the following are identities? Check all that apply.
    7·1 answer
  • (50) POINTS AND 5 STAR AND THANKS AND BRAIN-LIST
    10·1 answer
  • 24 rounded to the nearest hundred​
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!