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Roots of equation 2x²+3x+7=0 are a and b. The value of ab-¹+ba-¹ is?
Most Upvoted Answer
Roots of equation 2x²+3x+7=0 are a and b. The value of ab-¹+ba-¹ is?
To find values of (a/b)+(b/a)
some of the roots = -3/2
product of the roots = 7/2
(a/b)+(b/a)
= (a²+b²)/(ab)
=[(a+b)² - 2ab]/(ab)
=[(-3/2)² - 2(7/2)]/(7/2)
=(9/4 - 7)/(7/2)
= (-19/4)/(7/2)
= -19/14
thus,
(a/b)+(b/a)= -19/14
some of the roots = -3/2
product of the roots = 7/2
(a/b)+(b/a)
= (a²+b²)/(ab)
=[(a+b)² - 2ab]/(ab)
=[(-3/2)² - 2(7/2)]/(7/2)
=(9/4 - 7)/(7/2)
= (-19/4)/(7/2)
= -19/14
thus,
(a/b)+(b/a)= -19/14
Community Answer
Roots of equation 2x²+3x+7=0 are a and b. The value of ab-¹+ba-¹ is?
Explanation:
Given equation:
Given equation is 2x² + 3x + 7 = 0. Let the roots of the equation be a and b.
Finding the value of ab⁻¹ + ba⁻¹:
To find the value of ab⁻¹ + ba⁻¹, we need to first find the value of a⁻¹ and b⁻¹.
Since a and b are the roots of the equation 2x² + 3x + 7 = 0, we can use the sum and product of roots formula to find a and b.
Sum of roots (a + b) = -b/a = -3/2
Product of roots (ab) = c/a = 7/2
Now, we can find the values of a⁻¹ and b⁻¹:
a⁻¹ = 1/a = 1/(ab) = 2/7
b⁻¹ = 1/b = 1/(ab) = 2/7
Now, we can find the value of ab⁻¹ + ba⁻¹:
ab⁻¹ + ba⁻¹ = ab(1/a) + ba(1/b) = 2/7 + 2/7 = 4/7
Therefore, the value of ab⁻¹ + ba⁻¹ is 4/7.
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Roots of equation 2x²+3x+7=0 are a and b. The value of ab-¹+ba-¹ is?
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Roots of equation 2x²+3x+7=0 are a and b. The value of ab-¹+ba-¹ is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Roots of equation 2x²+3x+7=0 are a and b. The value of ab-¹+ba-¹ is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Roots of equation 2x²+3x+7=0 are a and b. The value of ab-¹+ba-¹ is?.
Roots of equation 2x²+3x+7=0 are a and b. The value of ab-¹+ba-¹ is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Roots of equation 2x²+3x+7=0 are a and b. The value of ab-¹+ba-¹ is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Roots of equation 2x²+3x+7=0 are a and b. The value of ab-¹+ba-¹ is?.
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