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The value of a for which the sum of the squares of the roots of the equation x2 – (a – 2)x – a – 1 = 0 assume the least value is
- a)2
- b)3
- c)0
- d)1
Correct answer is option 'D'. Can you explain this answer?
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The value of a for which the sum of the squares of the roots of the eq...
The equation is x^2 - ax + a = 0.
Let's denote the roots of this equation as r1 and r2.
By Vieta's formulas, we know that the sum of the roots is r1 + r2 = a and the product of the roots is r1 * r2 = a.
We are given that the sum of the squares of the roots is 36. Therefore, we have:
r1^2 + r2^2 = 36.
We can express r1^2 + r2^2 in terms of the sum and product of the roots using the following identity:
(r1 + r2)^2 - 2(r1 * r2) = r1^2 + r2^2.
Substituting the given values, we have:
(36) - 2(a) = 36.
Simplifying, we get:
36 - 2a = 36.
Subtracting 36 from both sides, we have:
-2a = 0.
Dividing both sides by -2, we get:
a = 0.
Therefore, the value of a for which the sum of the squares of the roots is 36 is a = 0.
Let's denote the roots of this equation as r1 and r2.
By Vieta's formulas, we know that the sum of the roots is r1 + r2 = a and the product of the roots is r1 * r2 = a.
We are given that the sum of the squares of the roots is 36. Therefore, we have:
r1^2 + r2^2 = 36.
We can express r1^2 + r2^2 in terms of the sum and product of the roots using the following identity:
(r1 + r2)^2 - 2(r1 * r2) = r1^2 + r2^2.
Substituting the given values, we have:
(36) - 2(a) = 36.
Simplifying, we get:
36 - 2a = 36.
Subtracting 36 from both sides, we have:
-2a = 0.
Dividing both sides by -2, we get:
a = 0.
Therefore, the value of a for which the sum of the squares of the roots is 36 is a = 0.
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The value of a for which the sum of the squares of the roots of the equation x2–(a –2)x –a –1 = 0 assume the least value isa)2b)3c)0d)1Correct answer is option 'D'. Can you explain this answer?
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The value of a for which the sum of the squares of the roots of the equation x2–(a –2)x –a –1 = 0 assume the least value isa)2b)3c)0d)1Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The value of a for which the sum of the squares of the roots of the equation x2–(a –2)x –a –1 = 0 assume the least value isa)2b)3c)0d)1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value of a for which the sum of the squares of the roots of the equation x2–(a –2)x –a –1 = 0 assume the least value isa)2b)3c)0d)1Correct answer is option 'D'. Can you explain this answer?.
The value of a for which the sum of the squares of the roots of the equation x2–(a –2)x –a –1 = 0 assume the least value isa)2b)3c)0d)1Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The value of a for which the sum of the squares of the roots of the equation x2–(a –2)x –a –1 = 0 assume the least value isa)2b)3c)0d)1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value of a for which the sum of the squares of the roots of the equation x2–(a –2)x –a –1 = 0 assume the least value isa)2b)3c)0d)1Correct answer is option 'D'. Can you explain this answer?.
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