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If and
are the roots of x2=x+1 then the value of
2 2
is:
(a)
2 5
(b)
5
(c)
3 5
(d)?
are the roots of x2=x+1 then the value of
2 2
is:
(a)
2 5
(b)
5
(c)
3 5
(d)?
Most Upvoted Answer
If and are the roots of x2=x+1 then the value of 2 2 is: (...
Solution:
Given:
- Let α and β be the roots of the equation x^2 = x + 1.
Formula:
- Sum of roots (α + β) = -b/a
- Product of roots (αβ) = c/a
Calculation:
- Given equation: x^2 = x + 1
- Rearranging, we get x^2 - x - 1 = 0
- Comparing with the general form ax^2 + bx + c = 0, we have a = 1, b = -1, c = -1
Sum of roots (α + β):
- Using the formula, we get α + β = -(-1)/1 = 1
Product of roots (αβ):
- Using the formula, we get αβ = -1/1 = -1
Value of αβ - βα:
- Substituting the values, we get αβ - βα = -1 - 1 = -2
Therefore, the value of αβ - βα is -2.
Given:
- Let α and β be the roots of the equation x^2 = x + 1.
Formula:
- Sum of roots (α + β) = -b/a
- Product of roots (αβ) = c/a
Calculation:
- Given equation: x^2 = x + 1
- Rearranging, we get x^2 - x - 1 = 0
- Comparing with the general form ax^2 + bx + c = 0, we have a = 1, b = -1, c = -1
Sum of roots (α + β):
- Using the formula, we get α + β = -(-1)/1 = 1
Product of roots (αβ):
- Using the formula, we get αβ = -1/1 = -1
Value of αβ - βα:
- Substituting the values, we get αβ - βα = -1 - 1 = -2
Therefore, the value of αβ - βα is -2.
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If and are the roots of x2=x+1 then the value of 2 2 is: (a) 2 5 (b) 5 (c) 3 5 (d)?
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If and are the roots of x2=x+1 then the value of 2 2 is: (a) 2 5 (b) 5 (c) 3 5 (d)? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If and are the roots of x2=x+1 then the value of 2 2 is: (a) 2 5 (b) 5 (c) 3 5 (d)? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If and are the roots of x2=x+1 then the value of 2 2 is: (a) 2 5 (b) 5 (c) 3 5 (d)?.
If and are the roots of x2=x+1 then the value of 2 2 is: (a) 2 5 (b) 5 (c) 3 5 (d)? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If and are the roots of x2=x+1 then the value of 2 2 is: (a) 2 5 (b) 5 (c) 3 5 (d)? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If and are the roots of x2=x+1 then the value of 2 2 is: (a) 2 5 (b) 5 (c) 3 5 (d)?.
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