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
ipn [44]
3 years ago
13

. If a, b, c are real numbers such that ac # 0

Mathematics
1 answer:
galben [10]3 years ago
7 0

Answer:

  if one equation has no real roots, the other must have real roots. Hence, at least one equation has real roots.

Step-by-step explanation:

The discriminant of the first equation is ...

  d1 = b^2 -4ac

The discriminant of the second equation is ...

  d2 = b^2 +4ac

__

Suppose the first equation has no real roots. Then ...

  d1 < 0

  b^2 -4ac < 0

  b^2 < 4ac

We know that b^2 is non-negative, so this means 4ac is positive. For that case,

  d2 = b^2 +4ac

is the sum of a positive number and a non-negative number so will be positive. When the discriminant is positive, there are two real roots.

When the first equation has no real roots, the second one must have two real roots.

__

Suppose the second equation has no real roots. Then ...

  d2 < 0

  b^2 +4ac < 0

  b^2 < -4ac

Again, b^2 is non-negative, so -4ac must be positive. For this case, the sum ...

  d1 = b^2 -4ac

is the sum of a non-negative and a positive number, so will be positive. The positive discriminant means there are two real roots.

When the second equation has no real roots, the first one must have two real roots.

One of these equations will have real roots, or not. If not, the other must have (distinct) real roots.

You might be interested in
What is the quotient of 2 1/5 ÷ 6 3/5 <br><br>A. 1/3<br><br>B. 3/4<br><br>C. 24/35<br><br>D. 2/3​
zepelin [54]

Answer:

A.1/3

Step-by-step explanation:

on the picture

if it's helpful ❤❤❤

THANK YOU.

7 0
2 years ago
Two friends are reading the same book. Amy can read 3 pages per minute, and she has already read 9 pages. Sam, who has a reading
Daniel [21]
Amy:  (3 pages/min)(x min) + 9 pages
Sam:  (2 pages/min)(x min)  + 47 pages

Equate these:  3x+9 = 2x + 47

Then x = 38.  The two friends will have covered the same number of pages after 38 minutes.  How many pages would that be?  3(38)+9 = 123 pages.
5 0
3 years ago
Help now solve it but show your work too
marin [14]

Answer:

-1/6

Step-by-step explanation:

1/6-1/3

1/6-1×2/3×2

1/6-2/6

1-2/6

-1/6

5 0
3 years ago
Read 2 more answers
Solve the following equation <br> T/4 +7 =2.
Sindrei [870]

Answer:

T=-20

Step-by-step explanation:

first get rid of the 7

1. T/4=-5

then multiply by 4 to isolate T

2. T=-20

4 0
3 years ago
Read 2 more answers
Felipe has 28 shirts to fold. Let N be the number of shirts he would have left to fold after folding F of them.
Debora [2.8K]
Ok let’s say he folds N=14 so F would be the other q4
8 0
3 years ago
Other questions:
  • 2/5(d−10)−2/3(d+6) is
    10·1 answer
  • Please help no one answers my questions :'(
    12·1 answer
  • What is the parent function of<br> f(x)=2/5(-x-5)^5 +2
    6·1 answer
  • The stem-and-leaf plot lists the number of times different families visit the local zoo each year. How many families visit the z
    15·1 answer
  • Y=0.27x constant of proportionality
    7·1 answer
  • Mark works as a librarian and makes $16.75 per hour. He gets paid time-and-a-half for overtime. How much will he make if he work
    6·1 answer
  • I need help plz!!!!<br> I need help plz!!!
    12·1 answer
  • Can anyone help me? I have to write an equation.
    10·1 answer
  • 40 POINTS please help
    5·2 answers
  • NEED HELP I need to fill in the highlighted parts
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!