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
patterns A and B are generated using these rules pattern a start with 12 and add six pattern be start with 4 and add 2​
JulsSmile [24]
5 after five turns of patti
8 0
3 years ago
A polyhedron with one pentagonal base is a
alekssr [168]
I think it is an apex
3 0
3 years ago
Need help with 9-12 plzzzzz
Vladimir79 [104]
Hi Lexia it's Aliyah
4 0
3 years ago
Read 2 more answers
The principal of the school is looking over grade reports, specifically scores on math quizzes.
guapka [62]

Answer:

Range = 45

Median = 75

Step-by-step explanation:

Based on the attached box and whisker plot :

From the plot :

Maximum value = 95

Minimum value = 50

The median value can be obtained from the box and whisker plot. The median value from the plot is ; the green dotted point inside the box :

This point is marked 75.

Hence, median value = 75

Range = maximum - minimum

Range =. 95 - 50 = 45

8 0
3 years ago
Hi could you please help? Write 2.96 as a mixed number or fraction in simplest form. My family is trying to help me but we're ba
klemol [59]

as a fraction it would be 74 over 25 in one way there might be other ways


3 0
3 years ago
Read 2 more answers
Other questions:
  • Find the fifth roots of 243(cos 260° + i sin 260°)
    5·1 answer
  • 8 + 6x - 10x = 16 - 8x
    5·1 answer
  • Lisa walked 48 blocks in 3 hours how much blocks per hours
    5·1 answer
  • Equation that would have infinitely many solutions with 5x+3y=12
    5·1 answer
  • (3 - (-4) x) 2, when x = 3
    12·2 answers
  • 3. Given: ZCAT and ZDOG are right angles.<br> What are ALL the conclusions that can be made?
    14·1 answer
  • 0.90[2.25[4]+1.40[3]+6]
    15·1 answer
  • Do the ratios 4/ 10 and 1/ 2 form a proportion?
    14·2 answers
  • Margo can purchase tile at a store for $0.99 per tile and rent a tile saw for $18. At another store she can
    10·1 answer
  • How many minutes make a hour
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!