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If alpha ,beta are the roots of quadratic equation 2x^2 x-1=0 then find the value of alpha square beta square?
Most Upvoted Answer
If alpha ,beta are the roots of quadratic equation 2x^2 x-1=0 then fin...
Solution:
Given equation is 2x^2 x-1=0.
Let's solve the given equation to find the roots.
Step 1: Write the given equation as 2x^2 = 1.
Step 2: Divide both sides of the equation by 2 to get x^2 = 1/2.
Step 3: Take the square root of both sides of the equation to get x = ±(1/√2).
Therefore, the roots of the equation are α = 1/√2 and β = -1/√2.
To find the value of α^2β^2, we need to substitute the values of α and β in the expression and simplify.
Step 1: α^2β^2 = (1/√2)^2(-1/√2)^2.
Step 2: Simplify the expression to get α^2β^2 = 1/4.
Therefore, the value of α^2β^2 is 1/4.
Final Answer: α^2β^2 = 1/4.
Given equation is 2x^2 x-1=0.
Let's solve the given equation to find the roots.
Step 1: Write the given equation as 2x^2 = 1.
Step 2: Divide both sides of the equation by 2 to get x^2 = 1/2.
Step 3: Take the square root of both sides of the equation to get x = ±(1/√2).
Therefore, the roots of the equation are α = 1/√2 and β = -1/√2.
To find the value of α^2β^2, we need to substitute the values of α and β in the expression and simplify.
Step 1: α^2β^2 = (1/√2)^2(-1/√2)^2.
Step 2: Simplify the expression to get α^2β^2 = 1/4.
Therefore, the value of α^2β^2 is 1/4.
Final Answer: α^2β^2 = 1/4.
Community Answer
If alpha ,beta are the roots of quadratic equation 2x^2 x-1=0 then fin...
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If alpha ,beta are the roots of quadratic equation 2x^2 x-1=0 then find the value of alpha square beta square?
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If alpha ,beta are the roots of quadratic equation 2x^2 x-1=0 then find the value of alpha square beta square? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If alpha ,beta are the roots of quadratic equation 2x^2 x-1=0 then find the value of alpha square beta square? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha ,beta are the roots of quadratic equation 2x^2 x-1=0 then find the value of alpha square beta square?.
If alpha ,beta are the roots of quadratic equation 2x^2 x-1=0 then find the value of alpha square beta square? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If alpha ,beta are the roots of quadratic equation 2x^2 x-1=0 then find the value of alpha square beta square? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha ,beta are the roots of quadratic equation 2x^2 x-1=0 then find the value of alpha square beta square?.
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