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
Brilliant_brown [7]
3 years ago
13

Use the discriminant to determine what type of roots the equations will have, and categorize the equations according to their ro

ots.
two distinct roots, One repeated root, two complex roots



x^2 − 4x + 2 = 0

5x^2 − 2x + 3 = 0

2x^2 + x − 6 = 0

13x^2 − 4 = 0

x^2 − 6x + 9 = 0

x^2 − 8x + 16 = 0

4x^2 + 11 = 0
Mathematics
2 answers:
lilavasa [31]3 years ago
8 0

Answer:

For the equation x2 − 4x + 2 = 0, the discriminant is (-4)2 − 4(1)(2) = 8. Since the discriminant is positive, it has two distinct real roots.

For the equation 5x2 − 2x + 3 = 0, the discriminant is (-2)2 − 4(5)(3) = -56. Since the discriminant is negative, it has two complex roots.

For the equation 2x2 + x − 6 = 0, the discriminant is (1)2 − 4(2)(-6) = 49. Since the discriminant is positive, it has two distinct real roots.

For the equation 13x2 − 4 = 0, the discriminant is (0)2 − 4(13)(-4) = 208. Since the discriminant is positive, it has two distinct real roots.

For the equation x2 − 6x + 9 = 0, the discriminant is (-6)2 − 4(1)(9) = 0. Since the discriminant is zero, it has one repeated root.

For the equation x2 − 8x + 16 = 0, the discriminant is (-8)2 − 4(1)(16) = 0. Since the discriminant is zero, it has one repeated root.

For the equation 4x2 + 11 = 0, the discriminant is (0)2 − 4(4)(11) = -176. Since the discriminant is negative, it has two complex roots.

topjm [15]3 years ago
6 0

Step-by-step explanation:

The discriminant of the quadratic equation ax^2+bx+c=0:

\Delta=b^2-4ac

If Δ < 0, then the equation has two complex roots x=\dfrac{-b\pm\sqrt\Delta}{2a}

If Δ = 0, then the equation has one repeated root x=\dfrac{-b}{2a}[/tex If Δ > 0, then the equation has two discint roots [tex]x=\dfrac{-b\pm\sqrt\Delta}{2a}

1.\ x^2-4x+2=0\\\\a=1,\ b=-4,\ c=2\\\\\Delta=(-4)^2-4(1)(2)=16-8=8>0,\ \bold{two\ distinct\ roots}\\\sqrt\Delta=\sqrt8=\sqrt{4\cdot2}=2\sqrt2\\\\x=\dfrac{-(-4)\pm2\sqrt2}{2(1)}=\dfrac{4\pm2\sqrt2}{2}=2\pm\sqrt2\\\\==============================\\\\2.\ 5x^2-2x+3=0\\\\a=5,\ b=-2,\ c=3\\\\\Delta=(-2)^2-4(5)(3)=4-60=-56

3.\ 2x^2+x-6=0\\\\a=2,\ b=1,\ c=-6\\\\\Delta=1^2-4(2)(-6)=1+48=49>0,\ \bold{two\ distinct\ roots}\\\sqrt\Delta=\sqrt{49}=7\\\\x=\dfrac{-1\pm7}{(2)(2)}\\\\x_1=\dfrac{-8}{4}=-2,\ x_2=\dfrac{6}{4}=\dfrac{3}{2}\\\\==============================\\\\4.\ 13x^2-4=0\qquad\text{add 4 to both sides}\\\\13x^2=4\qquad\text{divide both sides by 13}\\\\x^2=\dfrac{4}{13}\to x=\pm\sqrt{\dfrac{4}{13}},\ \bold{two\ distinct\ roots}\\\\==============================

5.\ x^2-6x+16=0\\\\a=1,\ b=-6,\ c=16\\\\\Delta=(-6)^2-4(1)(16)=36-64=-28

7.\ 4x^2+11=0\qquad\text{subtract 11 from both sides}\\\\4x^2=-11\qquad\text{divide both sides by 4}\\\\x^2=-\dfrac{11}{4}\to x=\pm\sqrt{-\dfrac{11}{4}}\\\\x=\pm\dfrac{\sqrt{11}}{2}\ i,\ \bold{two\ complex\ roots}

You might be interested in
A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material for the sides of the can costs
PSYCHO15rus [73]

Answer:

the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm

Step-by-step explanation:

since the volume of a cylinder is

V= π*R²*L → L =V/ (π*R²)

the cost function is

Cost = cost of side material * side area  + cost of top and bottom material * top and bottom area

C = a* 2*π*R*L + b* 2*π*R²

replacing the value of L

C = a* 2*π*R* V/ (π*R²) + b* 2*π*R²  = a* 2*V/R + b* 2*π*R²

then the optimal radius for minimum cost can be found when the derivative of the cost with respect to the radius equals 0 , then

dC/dR = -2*a*V/R² + 4*π*b*R = 0

4*π*b*R = 2*a*V/R²

R³ = a*V/(2*π*b)

R=  ∛( a*V/(2*π*b))

replacing values

R=  ∛( a*V/(2*π*b)) = ∛(0.03$/cm² * 600 cm³ /(2*π* 0.05$/cm²) )= 3.85 cm

then

L =V/ (π*R²) = 600 cm³/(π*(3.85 cm)²) = 12.88 cm

therefore the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm

5 0
3 years ago
Find the percent error in this situation<br> Estimated: 145<br> Actual value: 189
levacccp [35]

Answer:

-23.2

                                        _____      _____

hello thre um                   ((_O_))     ((_O_))

                                             ///     v    ///

3 0
3 years ago
Donald is 38 years younger than Natalie. 5 years ago, Natalie's age was 3 times Donald's age. How old is Donald now?
Svetlanka [38]

9514 1404 393

Answer:

  24

Step-by-step explanation:

Let d represent Donald's age now. Then Natali's age now is d+38. The age relationship 5 years ago was ...

  (d+38) -5 = 3(d -5)

  d +33 = 3d -15 . . . . . eliminate parentheses

  48 = 2d . . . . . . . . . . . add 15-d

  24 = d . . . . . . . . . . . . . divide by 2

Donald is 24 years old now.

_____

<em>Alternate solution</em>

You can also work this by considering that 5 years ago, Natalie's age was more than Donald's age by twice Donald's age then. Hence Donald was 38/2 = 19 at that time. Now, Donald is 19+5 = 24.

4 0
3 years ago
Chad is renting a moving van for one day. It costs $20 to rent the van for the day. It also costs $0.60 for each mile the van is
Volgvan

Answer:

20 + 0.6x

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Jin schedules 496 hours for a project. He plans to work 8 hours each day. How many days will it take to complete the project?​
Airida [17]

Answer:

62 days

Step-by-step explanation:

496/8 = 62

5 0
3 years ago
Read 2 more answers
Other questions:
  • The value -2 is a lower bound for the zeros of the function shown below.
    8·1 answer
  • Which scenario involves acceleration
    5·1 answer
  • What is the sum of the given polynomials in standard form ? (X^2-3x)+(-2x^2+5x-3)
    6·1 answer
  • Andrea has 35 beads total. She wants to make 5 necklaces. how many beads are going to be on each necklace
    8·2 answers
  • Someone please help with the Determine Rate of Change Question I’m gonna fail please help me
    15·1 answer
  • 10,9, 23, 68, 70, 4, 12,4<br> What is the median for this set of numbers?
    12·2 answers
  • Write an exponential function y = a(b)" whose graph passes through the given
    5·1 answer
  •  please HURRY I WILL GIVE BRAINLEST <br><br> Which expression is equivalent to -6 (3X-2/3)
    5·2 answers
  • Factorize = n!+(n-1)!
    5·1 answer
  • A solid has twelve more edges than faces. How many vertices does it have?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!