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If p and q are the roots of x
2
+ 2x + 1 = 0 then the values of p3
+ q3
becomes?
2
+ 2x + 1 = 0 then the values of p3
+ q3
becomes?
Most Upvoted Answer
If p and q are the roots of x 2 + 2x + 1 = 0 then the values of p3 +...
Given equation:
x^2 + 2x + 1 = 0
Finding the roots:
The given equation can be factored as (x + 1)^2 = 0
Therefore, the roots are p = q = -1
Finding p^3 + q^3:
Let's use the formula for the sum of cubes:
p^3 + q^3 = (p + q)(p^2 - pq + q^2)
Finding the sum of roots (p + q):
p + q = -1 + (-1) = -2
Finding the product of roots (pq):
p*q = (-1)(-1) = 1
Substitute values in the formula:
p^3 + q^3 = (-2)(p^2 - pq + q^2)
= -2[(p^2 + 2pq + q^2) - 3pq]
= -2[(p + q)^2 - 3pq]
= -2[(-2)^2 - 3(1)]
= -2[4 - 3]
= -2(1)
= -2
Therefore, the value of p^3 + q^3 is -2.
x^2 + 2x + 1 = 0
Finding the roots:
The given equation can be factored as (x + 1)^2 = 0
Therefore, the roots are p = q = -1
Finding p^3 + q^3:
Let's use the formula for the sum of cubes:
p^3 + q^3 = (p + q)(p^2 - pq + q^2)
Finding the sum of roots (p + q):
p + q = -1 + (-1) = -2
Finding the product of roots (pq):
p*q = (-1)(-1) = 1
Substitute values in the formula:
p^3 + q^3 = (-2)(p^2 - pq + q^2)
= -2[(p^2 + 2pq + q^2) - 3pq]
= -2[(p + q)^2 - 3pq]
= -2[(-2)^2 - 3(1)]
= -2[4 - 3]
= -2(1)
= -2
Therefore, the value of p^3 + q^3 is -2.
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If p and q are the roots of x 2 + 2x + 1 = 0 then the values of p3 + q3 becomes?
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If p and q are the roots of x 2 + 2x + 1 = 0 then the values of p3 + q3 becomes? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If p and q are the roots of x 2 + 2x + 1 = 0 then the values of p3 + q3 becomes? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If p and q are the roots of x 2 + 2x + 1 = 0 then the values of p3 + q3 becomes?.
If p and q are the roots of x 2 + 2x + 1 = 0 then the values of p3 + q3 becomes? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If p and q are the roots of x 2 + 2x + 1 = 0 then the values of p3 + q3 becomes? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If p and q are the roots of x 2 + 2x + 1 = 0 then the values of p3 + q3 becomes?.
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