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
MrRissso [65]
3 years ago
7

Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 -

6x + 5 y = x2 + 7x - 11 y = -x2 - 8x - 16 R
Mathematics
1 answer:
rosijanka [135]3 years ago
7 0

Answer:

Step-by-step explanation:

Our equations are

y = -3x^2 + x + 12\\y = 2x^2 - 6x + 5\\y = x^2 + 7x - 11\\y = -x^2 - 8x - 16\\

Let us understand the term Discriminant of a quadratic equation and its properties

Discriminant is denoted by  D and its formula is

D=b^2-4ac\\

Where

a= the coefficient of the x^{2}

b= the coefficient of x

c = constant term

Properties of D: If D

i) D=0 , One real root

ii) D>0 , Two real roots

iii) D<0 , no real root

Hence in the given quadratic equations , we will find the values of D Discriminant  and evaluate our answer accordingly .

Let us start with

y = -3x^2 + x + 12\\a=-3 , b =1 , c =12\\D=1^2-4*(-3)*(12)\\D=1+144\\D=145\\D>0 \\

Hence we have two real roots for this equation.

y = 2x^2 - 6x + 5\\

y = 2x^2 - 6x + 5\\a=2,b=-6,c=5\\D=(-6)^2-4*2*5\\D=36-40\\D=-4\\D

Hence we do not have any real root for this quadratic

y = x^2 + 7x - 11\\a=1,b=7,-11\\D=7^2-4*1*(-11)\\D=49+44\\D=93\\

Hence D>0 and thus we have two real roots for this equation.

y = -x^2 - 8x - 16\\a=-1,b=-8,c=-16\\D=(-8)^2-4*(-1)*(-16)\\D=64-64\\D=0\\

Hence we have one real root to this quadratic equation.

You might be interested in
Why is it ironic that the mother asks her child to go to church?
Yuki888 [10]

Answer:

Because most kids dont like going to church.

4 0
3 years ago
How do you get 7:46
Flauer [41]

Answer:8:26

Step-by-step explanation:you subtract what time it is by 1:34 then take away 60 for a hour and add it to a hour so taking 60 mins gives you a hour

6 0
3 years ago
Please help ASAP, giving brainliest!
scoundrel [369]

Answer:no

Step-by-step explanation:

Because you have two -2 in the x slots , if you see an number more than once it is no longer a function.

7 0
3 years ago
The ratio of students to adults on a field trip is 4 to 3. Which table correctly
Anit [1.1K]

Answer:

B

Step-by-step explanation:

Brainliest?

8 0
3 years ago
Read 2 more answers
A bridge is built in the shape of a semielliptical arch. The bridge has a span of 60 feet and a maximum height of 10 feet. Choos
Dennis_Churaev [7]
Is there a way you can send me a picture of what your copying your answer from ?
6 0
3 years ago
Other questions:
  • 1. A clerk at the pet store kept track of the number of fish purchased by customers during one week. Mary bought 1 fish, Ari bou
    11·2 answers
  • The distance in feet that Karina swims in a race is represented by 4d - 4, where is d is the distance for each lap. What is an e
    7·1 answer
  • Find 1,2,4 m angles
    13·2 answers
  • Angela Spangler credit card statement to purchase a new backpack for $28 and bought her sister birthday gift for $45 she made a
    10·1 answer
  • When 60% of a number is added to the number, the result is 208<br>​
    7·1 answer
  • The rate of people entering a safari tour is modeled by the equation p(t) = 200e ^ (- t) for the first 5 hoursEstimate the popul
    8·1 answer
  • Find the missing variable and indicated angle measure<br> Please help lol
    13·1 answer
  • A Salt Marsh Harvest Mouse ran a 360 centimeter straight course race in 9 seconds. How fast did it run?
    5·2 answers
  • Write the number 16, 107, 320 in expanded<br> form.
    9·1 answer
  • the half -life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mas
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!