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
lbvjy [14]
2 years ago
14

Write the quadratic equation whose roots are 1 and -5, and whose leading coefficient is 3.

Mathematics
1 answer:
Anna35 [415]2 years ago
7 0

Step-by-step explanation:

they're is a neat little trick.

but first of all, "roots" means the 0 solutions of the equation. like

ax² + bx + c = 0

there are 2 solutions for x to make the whole expression equal 0.

these are the "roots".

now to the little trick :

when is a multiplication resulting in 0 ?

when at least one of the factors is 0.

and any quadratic expression can be written as multiplication of 2 factors. like

c(x - a)(x - b) = cx² - cax - cbx + cab

what are the "roots" or 0 points ?

either

c = 0

x - a = 0 | x = a

x - b = 0 | x = b

the leading coefficient = 3.

that means nothing else than c = 3.

root = 1 means (x - 1) is one factor.

root = -5 means (x + 5) is the other factor.

so, we have

3(x - 1)(x + 5) = 3x² + 12x - 15

and the equation is

3x² + 12x - 15 = 0

or

3x² + 12x = 15

You might be interested in
Five members of the soccer team and five members of the track team ran the 100-meter dash. Their times are listed in the table b
Sonbull [250]
Soccer : (12.3 + 13.2 + 12.5 + 11.3 + 14.4) / 5 = 63.7 / 5 = 12.74
track : (12.3 + 11.2 + 11.7 + 12.2 + 13.7) / 5 = 61.1 / 5 = 12.22

difference is : 12.74 - 12.22 = 0.52 <=
3 0
3 years ago
Read 2 more answers
A car can travel 24 miles for every 1 gallon of gasoline.
jasenka [17]
The car can travel 235.2 miles on 9.8 gallons. Just multiply 24 by 9.8.
5 0
3 years ago
Hiros family lives 448 kilometers from the beach.Each of the 5 adults drove the family van an equal distance to get to and from
Drupady [299]

Answer:

179.2km

Step-by-step explanation:

The distance from their house to the beach is 448km. Now they have to drive to and from the beach. The total distance traveled by the family is 448km + 448km.

This is equal to 896km. Now we have 5 adults who took their turns to drive and they drove the same distance. The total distance traveled by each adult will be 896/5 = 179.2km

Hence, each adult in the family drove a distance of 179.2km

3 0
3 years ago
What is the time and space margin that is the distance you can see ahead of your vehicle?
IgorLugansk [536]
The space margin depends on light and weather conditions as well as terrain (road curvature, hills, trees or other obstacles).

The time margin depends on the space margin, your reaction time, and your speed of travel.

You may appear to have a lot of time or space in icy conditions, but that can be an illusion. A collision course on ice will result in a collision, regardless of the time or distance involved.

Insufficient information is provided to be more specific.
5 0
3 years ago
Mike and his dad are retiling his bathroom floor. They have budgeted $200 for the tiles and supplies. The tiles cost $1.85 each
Feliz [49]

Answer:

Equation: $114.90 + $1.85<em>x</em> = 200

Solution: They can buy 46 tiles.

Step-by-step explanation:

First, subtract 114.90 from both sides to get 1.85<em>x</em> = 85.10.

Divide 85.10 by 1.85 to get 46, which is the answer.

7 0
3 years ago
Other questions:
  • A grocery store has 5 pounds of granola. One customer buys 2/3 pound of granola and another buys 5/6 pound. After these purchase
    6·1 answer
  • A researcher has developed a new drug designed to reduce blood pressure. In an experiment, 21 subjects were assigned randomly to
    9·1 answer
  • Two planes are circling an airport awaiting their landing clearance. If the following measures in the diagram below are correct,
    9·2 answers
  • Which equation represents a line that passes through the two points in the table?
    9·1 answer
  • How many factors are in the expression 2w(w+9)
    9·1 answer
  • Evaluate the expression 9x , when x= 4, 7, and 2.5
    12·2 answers
  • Please help me! (please no links!)​
    11·2 answers
  • What is the slope in this graph?
    10·1 answer
  • A company's sales in Seattle were $330,000 in 2012, while their sales in Portland were $235,000 for the same year. Complete the
    14·1 answer
  • Natasha was thinking of a number.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!