SAT Exam > SAT Questions > What is the sum of all values that satisfy th...
Start Learning for Free
What is the sum of all values that satisfy the equation 3x2 + 30x + 15 = 0?
- a)-10
- b)− 4√5
- c)4√5
- d)10
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
What is the sum of all values that satisfy the equation 3x2 + 30x + 15...
The simplest way to solve this problem is to use the theorem that any quadratic equation in the form ax2 + bx + c = 0 has two (possibly equal) solutions that have a sum of -b/a and a product of c/a. Therefore the sum of the solutions to this equation is -30/3 = -10.
If you don't recall this theorem, you can solve it the hard way: by finding the two solutions with the Quadratic Formula and adding them together.
Use the quadratic formula,
Simplify:
Simplify the radical:
Reduce the fractions:
The two solutions are x = -5 + 2√5 and x = -5 - 2√5,
and their sum is (-5 - 2√5) + (-5 + 2√5) = -10.
If you don't recall this theorem, you can solve it the hard way: by finding the two solutions with the Quadratic Formula and adding them together.
Use the quadratic formula,
Simplify:
Simplify the radical:
Reduce the fractions:
The two solutions are x = -5 + 2√5 and x = -5 - 2√5,
and their sum is (-5 - 2√5) + (-5 + 2√5) = -10.
Most Upvoted Answer
What is the sum of all values that satisfy the equation 3x2 + 30x + 15...
To find the sum of all values that satisfy the equation, we need to find the roots of the equation.
We can factor out a common factor of 3 from the equation:
3(x^2 + 10x + 5) = 0
Now, we have a quadratic equation in the form ax^2 + bx + c = 0, where a = 1, b = 10, and c = 5.
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values, we get:
x = (-10 ± √(10^2 - 4(1)(5))) / (2(1))
= (-10 ± √(100 - 20)) / 2
= (-10 ± √80) / 2
= (-10 ± 4√5) / 2
= -5 ± 2√5
The two solutions are -5 + 2√5 and -5 - 2√5.
The sum of these two values is (-5 + 2√5) + (-5 - 2√5) = -10.
Therefore, the sum of all values that satisfy the equation is -10.
Answer: a) -10
We can factor out a common factor of 3 from the equation:
3(x^2 + 10x + 5) = 0
Now, we have a quadratic equation in the form ax^2 + bx + c = 0, where a = 1, b = 10, and c = 5.
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values, we get:
x = (-10 ± √(10^2 - 4(1)(5))) / (2(1))
= (-10 ± √(100 - 20)) / 2
= (-10 ± √80) / 2
= (-10 ± 4√5) / 2
= -5 ± 2√5
The two solutions are -5 + 2√5 and -5 - 2√5.
The sum of these two values is (-5 + 2√5) + (-5 - 2√5) = -10.
Therefore, the sum of all values that satisfy the equation is -10.
Answer: a) -10
|
Explore Courses for SAT exam
|
|
Top Courses for SATView all
What is the sum of all values that satisfy the equation 3x2 + 30x + 15 = 0?a)-10b)− 4√5c)4√5d)10Correct answer is option 'A'. Can you explain this answer?
Question Description
What is the sum of all values that satisfy the equation 3x2 + 30x + 15 = 0?a)-10b)− 4√5c)4√5d)10Correct answer is option 'A'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about What is the sum of all values that satisfy the equation 3x2 + 30x + 15 = 0?a)-10b)− 4√5c)4√5d)10Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the sum of all values that satisfy the equation 3x2 + 30x + 15 = 0?a)-10b)− 4√5c)4√5d)10Correct answer is option 'A'. Can you explain this answer?.
What is the sum of all values that satisfy the equation 3x2 + 30x + 15 = 0?a)-10b)− 4√5c)4√5d)10Correct answer is option 'A'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about What is the sum of all values that satisfy the equation 3x2 + 30x + 15 = 0?a)-10b)− 4√5c)4√5d)10Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the sum of all values that satisfy the equation 3x2 + 30x + 15 = 0?a)-10b)− 4√5c)4√5d)10Correct answer is option 'A'. Can you explain this answer?.
Solutions for What is the sum of all values that satisfy the equation 3x2 + 30x + 15 = 0?a)-10b)− 4√5c)4√5d)10Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for SAT.
Download more important topics, notes, lectures and mock test series for SAT Exam by signing up for free.
Here you can find the meaning of What is the sum of all values that satisfy the equation 3x2 + 30x + 15 = 0?a)-10b)− 4√5c)4√5d)10Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
What is the sum of all values that satisfy the equation 3x2 + 30x + 15 = 0?a)-10b)− 4√5c)4√5d)10Correct answer is option 'A'. Can you explain this answer?, a detailed solution for What is the sum of all values that satisfy the equation 3x2 + 30x + 15 = 0?a)-10b)− 4√5c)4√5d)10Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of What is the sum of all values that satisfy the equation 3x2 + 30x + 15 = 0?a)-10b)− 4√5c)4√5d)10Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice What is the sum of all values that satisfy the equation 3x2 + 30x + 15 = 0?a)-10b)− 4√5c)4√5d)10Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice SAT tests.
|
|
Explore Courses for SAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup