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
den301095 [7]
3 years ago
7

Use the quadratic formula to solve the following equation -3x^2-x-3=0

Mathematics
1 answer:
tigry1 [53]3 years ago
8 0

<u>Answer:</u>

x=-\frac{1}{6}-\frac{\sqrt{35}}{6} i \text { and } x=-\frac{1}{6}+\frac{\sqrt{35}}{6} i are two roots of equation -3 x^{2}-x-3=0

<u>Solution:</u>

Need to solve given equation using quadratic formula.

-3 x^{2}-x-3=0

General form of quadratic equation is a x^{2}+b x+c=0

And quadratic formula for getting roots of quadratic equation is

x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

In our case b = -1 , a = -3 and c = -3

Calculating roots of the equation we get

\begin{array}{l}{x=\frac{-(-1) \pm \sqrt{(-1)^{2}-4(-3)(-3)}}{2 \times-3}} \\\\ {x=-\frac{1}{6} \pm\left(-\frac{\sqrt{-35}}{6}\right)}\end{array}

Since b^{2}-4 a c is equal to -35, which is less than zero, so given equation will not have real roots and have complex roots.

\begin{array}{l}{\text { Hence } x=-\frac{1}{6}-\frac{\sqrt{35}}{6} i \text { and } x=-\frac{1}{6}+\frac{\sqrt{35}}{6} i \text { are two roots of equation - }} \\ {3 x^{2}-x-3=0}\end{array}

You might be interested in
A shoe box in the shape of a rectangular prism has a length of 12 inches, a width of 6 1/2 inches, and a height of 4 1/2 inches.
katovenus [111]
12 x 6 1/2 x 4 1/2 = 351in^3
3 0
3 years ago
Round 10.245 to the place that 2 is underlined
cricket20 [7]
10.20
BECAUSE IF YOU ROUND THE TENTHS 4 MEANS 0.  
6 0
2 years ago
Read 2 more answers
Find a quadratic equation whose roots are 1.5 +√2 and 1.5-√2expressing it in the form of ax^2+bx+c+c=0 where a,b and c are integ
Ilia_Sergeevich [38]

0 = f(x) = (x - r)(x - s) = x² - (r+s) + rs

We have r=1.5+√2,  s=1.5 -√2 so r+s = 3 and

rs = (1.5+√2)(1.5 - √2) = 1.5² - (√2)² = 2.25 - 2 = 0.25

f(x) = x² - 3x + -.25

For integer coefficients we mulitply by 4,

g(x) = 4f(x) = 4x² - 12x - 1

Answer:  4x² - 12x - 1 = 0

5 0
3 years ago
I NEED HELP!!! 21-22
Nesterboy [21]

21. P=118

21. Q=142

22. P=120

22. R=60

22. S=60

3 0
3 years ago
Add mix numbers Madison made a fruit salad . She used 3 1 fourth cups of straw berries and 2 1 fourths cups of blueberries. How
Zinaida [17]

Answer:

1 1/4

Step-by-step explanation:

For the strawberries, we will have to multiply 3 by 1/4 to get the total amount of strawberries used.

1/4 * 3 = 3/4

For the blueberries, we will have to multiply 2 by 1/4 to get the total amount of blueberries used.

1/4 * 2 = 2/4

Simplify that to get 1/2

Now we need to add 3/4 and 1/2

3/4 + 1/2 = 5/4

Simplify that and we get our answer;

1 1/4

7 0
3 years ago
Other questions:
  • The measure of the acute angles of the right triangle below are represented by x and y. In this triangle y is 15 less twice x
    6·1 answer
  • Lena had $12. She bought a pack of craft paper for $6 and a sharpener for $2. Which expression correctly shows the total money L
    11·2 answers
  • What is the GCF of 60<br> and 24?<br> What is the answer for this question though?
    14·1 answer
  • Snapdragon plants have a gene that determines the presence of chlorophyll. The dominant allele (C) causes the plant to make chlo
    13·1 answer
  • 38 divided by 3576 long division<br><img src="https://tex.z-dn.net/?f=38%20%5Csqrt%7B3576%7D%20" id="TexFormula1" title="38 \sqr
    5·1 answer
  • Find the answer to: 2/3 +1/6
    6·1 answer
  • Which of the following shows the reflection?
    11·2 answers
  • What is the mean absolute deviation of the data set? Use paper and pencil,
    11·1 answer
  • One number is seven less than four times the other number. The sum of the two numbers is 93. Find the numbers.
    6·1 answer
  • Write a rule for the linear function in the table.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!