Software Development Exam > Software Development Questions > If α and β are the roots of the equation x2 -... Start Learning for Free
If α and β are the roots of the equation x2 - 7x + 1 = 0, then what is the value of
α4
+β4
?- a)2207
- b)2247
- c)2317
- d)2337
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If α and β are the roots of the equation x2 - 7x + 1 = 0, then what is...
Concept:
1.
For the quadratic equation ax2
+ bx + c = 0Sum of root (α + β) = -b/a
Product of root = c/a
2.
a2 + b2
= (a + b)2
- 2ab3.
a4
+
b4
= (a2 + b2)
2
- 2(
ab)2
Calculation:
x
2
- 7x + 1 = 0As α & β be roots of the quadratic equation
α + β =
-(-7)/1α + β
= 7
αβ = 1
By using the above identity
α2 + β2 = (α + β)2 - 2αβ = 72 - 2
α
2
+ β
2
= 47Now we can use the identity:
α4 + β4 =
(α
2
+ β
2
)
2
- 2α
2
β
2
Substituting in the value of α2 + β2 and αβ = 1, we get:
α44 + β4 = (47)2 - 2 = 2207
∴ The value of α
4
+ β4
is 2207.Most Upvoted Answer
If α and β are the roots of the equation x2 - 7x + 1 = 0, then what is...
Given Equation:
The equation given is x^2 - 7x + 1 = 0. Let α and β be the roots of this equation.
Sum and Product of Roots:
From the equation x^2 - 7x + 1 = 0, we know that the sum of the roots (α + β) = 7 and the product of the roots (αβ) = 1.
Using Vieta's Formulas:
We can express α^4 + β^4 in terms of α + β and αβ using the following formula:
α^4 + β^4 = (α^2 + β^2)^2 - 2α^2β^2
We know that (α + β)^2 = α^2 + β^2 + 2αβ
Therefore, α^2 + β^2 = (α + β)^2 - 2αβ
Substitute the values, we get:
α^2 + β^2 = 7^2 - 2(1) = 49 - 2 = 47
Calculating α^4 + β^4:
Now, we can find α^4 + β^4 using the formula:
α^4 + β^4 = (α^2 + β^2)^2 - 2α^2β^2
α^4 + β^4 = 47^2 - 2(1)^2
α^4 + β^4 = 2209 - 2 = 2207
Conclusion:
Therefore, the value of α^4 + β^4 is 2207, which corresponds to option 'A'.
The equation given is x^2 - 7x + 1 = 0. Let α and β be the roots of this equation.
Sum and Product of Roots:
From the equation x^2 - 7x + 1 = 0, we know that the sum of the roots (α + β) = 7 and the product of the roots (αβ) = 1.
Using Vieta's Formulas:
We can express α^4 + β^4 in terms of α + β and αβ using the following formula:
α^4 + β^4 = (α^2 + β^2)^2 - 2α^2β^2
We know that (α + β)^2 = α^2 + β^2 + 2αβ
Therefore, α^2 + β^2 = (α + β)^2 - 2αβ
Substitute the values, we get:
α^2 + β^2 = 7^2 - 2(1) = 49 - 2 = 47
Calculating α^4 + β^4:
Now, we can find α^4 + β^4 using the formula:
α^4 + β^4 = (α^2 + β^2)^2 - 2α^2β^2
α^4 + β^4 = 47^2 - 2(1)^2
α^4 + β^4 = 2209 - 2 = 2207
Conclusion:
Therefore, the value of α^4 + β^4 is 2207, which corresponds to option 'A'.
 | Explore Courses for Software Development exam |  |
Top Courses for Software DevelopmentView all
Top Courses for Software Development
Question Description
If α and β are the roots of the equation x2 - 7x + 1 = 0, then what is the value of α4 + β4 ? a)2207b)2247c)2317d)2337Correct answer is option 'A'. Can you explain this answer? for Software Development 2026 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about If α and β are the roots of the equation x2 - 7x + 1 = 0, then what is the value of α4 + β4 ? a)2207b)2247c)2317d)2337Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Software Development 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α and β are the roots of the equation x2 - 7x + 1 = 0, then what is the value of α4 + β4 ? a)2207b)2247c)2317d)2337Correct answer is option 'A'. Can you explain this answer?.
If α and β are the roots of the equation x2 - 7x + 1 = 0, then what is the value of α4 + β4 ? a)2207b)2247c)2317d)2337Correct answer is option 'A'. Can you explain this answer? for Software Development 2026 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about If α and β are the roots of the equation x2 - 7x + 1 = 0, then what is the value of α4 + β4 ? a)2207b)2247c)2317d)2337Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Software Development 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α and β are the roots of the equation x2 - 7x + 1 = 0, then what is the value of α4 + β4 ? a)2207b)2247c)2317d)2337Correct answer is option 'A'. Can you explain this answer?.
Solutions for If α and β are the roots of the equation x2 - 7x + 1 = 0, then what is the value of α4 + β4 ? a)2207b)2247c)2317d)2337Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Software Development. Download more important topics, notes, lectures and mock test series for Software Development Exam by signing up for free.
Here you can find the meaning of If α and β are the roots of the equation x2 - 7x + 1 = 0, then what is the value of α4 + β4 ? a)2207b)2247c)2317d)2337Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of If α and β are the roots of the equation x2 - 7x + 1 = 0, then what is the value of α4 + β4 ? a)2207b)2247c)2317d)2337Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If α and β are the roots of the equation x2 - 7x + 1 = 0, then what is the value of α4 + β4 ? a)2207b)2247c)2317d)2337Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If α and β are the roots of the equation x2 - 7x + 1 = 0, then what is the value of α4 + β4 ? a)2207b)2247c)2317d)2337Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice If α and β are the roots of the equation x2 - 7x + 1 = 0, then what is the value of α4 + β4 ? a)2207b)2247c)2317d)2337Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Software Development tests.
| Explore Courses for Software Development exam | |
Top Courses for Software Development
Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
