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
MatroZZZ [7]
2 years ago
10

What are the solutions to this quadratic equation? x2+6x-5 A. B. C. D.

Mathematics
1 answer:
faltersainse [42]2 years ago
4 0
Factoring x2-6x+5

The first term is, x2 its coefficient is 1 .
The middle term is, -6x its coefficient is -6 .
The last term, "the constant", is +5

Step-1 : Multiply the coefficient of the first term by the constant 1 • 5 = 5

Step-2 : Find two factors of 5 whose sum equals the coefficient of the middle term, which is -6 .

-5 + -1 = -6 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and -1
x2 - 5x - 1x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
1 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x-1) • (x-5)
Which is the desired factorization

Equation at the end of step
1
:

(x - 1) • (x - 5) = 0
STEP
2
:
Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : x-1 = 0

Add 1 to both sides of the equation :
x = 1

Solving a Single Variable Equation:

2.3 Solve : x-5 = 0

Add 5 to both sides of the equation :
x = 5

Supplement : Solving Quadratic Equation Directly

Solving x2-6x+5 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = x2-6x+5

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 3.0000

Plugging into the parabola formula 3.0000 for x we can calculate the y -coordinate :
y = 1.0 * 3.00 * 3.00 - 6.0 * 3.00 + 5.0
or y = -4.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2-6x+5
Axis of Symmetry (dashed) {x}={ 3.00}
Vertex at {x,y} = { 3.00,-4.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = { 1.00, 0.00}
Root 2 at {x,y} = { 5.00, 0.00}
You might be interested in
If 2x-10=4, what must x squelch to?
mr_godi [17]

Answer:

x=7

Step-by-step explanation:

2x-10=4 add 10 to both sides

2x=14 divide both sides by 2

x=7

3 0
3 years ago
I need help : (((((((
Allisa [31]

the answer is x=-1/3

7 0
2 years ago
Given the following triangle, if a = 2 and b = 3, find c.<br> √5<br> √10<br> √13
Tems11 [23]
We can use pythagorean theorem:

a^2 + b^2 = c^2

4 + 9 = c^2

13 = c^2

sqrt of 13 = c

Hope this helps!
4 0
3 years ago
Read 2 more answers
-3x-3y=3 and y=5x-17
Vesna [10]
The answer for this question is "y = -5/3 and x = 8/3"
5 0
3 years ago
Pablo is a technical writer who works 7.5 hours per day. He spends twice as much time on writing tasks as he does on other work
NikAS [45]
Pablo spends 15 hours on writing tasks
answer: twice as much=2 times this number
then twice as much= 7.5 times 2
7.5 times 2= 15hrs
6 0
3 years ago
Other questions:
  • Please help asap (:
    15·2 answers
  • What are the steps to simplifying radical expressions?​
    13·1 answer
  • A grasshopper has a length of (5x - 2) inches. A spider has a length of (2x - 1) inches. How much longer is the grasshopper?
    10·1 answer
  • Rounding or compatible numbers to estimate the difference. 762-332
    13·1 answer
  • 19. Which of the following is a correct
    14·1 answer
  • Please help and give right answers please!
    15·1 answer
  • Can y’all plz solve this
    9·2 answers
  • Evaluate f(3) for the function |-2x+1|
    14·1 answer
  • PLEASE HELP ME ASAP I'M BEING TIMED!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    9·2 answers
  • PLEASE HELP I NEED HELP
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!