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The roots of the equation x2 – 2 √2x + 1 = 0 are
- a)Real and different
- b)Imaginary and different
- c)Real and equal
- d)Rational and different
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The roots of the equation x2 – 2 √2x + 1 = 0 area)Real and...
The discriminant of the equation
( -2√2)2 – 4 (1) (1) = 8 – 4 = 4 > 0 and a perfect square, so roots are real and different but we can't say that roots are rational because coefficients are not rational therefore.
this is irrational
∴ the roots are real and different.
( -2√2)2 – 4 (1) (1) = 8 – 4 = 4 > 0 and a perfect square, so roots are real and different but we can't say that roots are rational because coefficients are not rational therefore.
this is irrational
∴ the roots are real and different.
Most Upvoted Answer
The roots of the equation x2 – 2 √2x + 1 = 0 area)Real and...
Understanding the Equation
The equation given is x² - 2√2x + 1 = 0. To determine the nature of its roots, we will use the discriminant method from the quadratic formula.
Quadratic Formula Overview
For a quadratic equation in the form ax² + bx + c = 0, the roots can be found using:
- Roots = (-b ± √(b² - 4ac)) / 2a
The term under the square root, known as the discriminant (D), determines the nature of the roots:
- D = b² - 4ac
Calculating the Discriminant
In our case:
- a = 1
- b = -2√2
- c = 1
Let's calculate the discriminant:
- D = (-2√2)² - 4(1)(1)
- D = (4 * 2) - 4
- D = 8 - 4
- D = 4
Interpreting the Discriminant
The results of the discriminant help us classify the roots:
- If D > 0, the roots are real and different.
- If D = 0, the roots are real and equal.
- If D < 0,="" the="" roots="" are="" />
Since we found D = 4, which is greater than 0, we conclude that:
Conclusion
- The roots of the equation x² - 2√2x + 1 = 0 are real and different.
Thus, the answer is option 'A' as stated.
The equation given is x² - 2√2x + 1 = 0. To determine the nature of its roots, we will use the discriminant method from the quadratic formula.
Quadratic Formula Overview
For a quadratic equation in the form ax² + bx + c = 0, the roots can be found using:
- Roots = (-b ± √(b² - 4ac)) / 2a
The term under the square root, known as the discriminant (D), determines the nature of the roots:
- D = b² - 4ac
Calculating the Discriminant
In our case:
- a = 1
- b = -2√2
- c = 1
Let's calculate the discriminant:
- D = (-2√2)² - 4(1)(1)
- D = (4 * 2) - 4
- D = 8 - 4
- D = 4
Interpreting the Discriminant
The results of the discriminant help us classify the roots:
- If D > 0, the roots are real and different.
- If D = 0, the roots are real and equal.
- If D < 0,="" the="" roots="" are="" />
Since we found D = 4, which is greater than 0, we conclude that:
Conclusion
- The roots of the equation x² - 2√2x + 1 = 0 are real and different.
Thus, the answer is option 'A' as stated.
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The roots of the equation x2 – 2 √2x + 1 = 0 area)Real and differentb)Imaginary and differentc)Real and equald)Rational and differentCorrect answer is option 'A'. Can you explain this answer?
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The roots of the equation x2 – 2 √2x + 1 = 0 area)Real and differentb)Imaginary and differentc)Real and equald)Rational and differentCorrect answer is option 'A'. 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 roots of the equation x2 – 2 √2x + 1 = 0 area)Real and differentb)Imaginary and differentc)Real and equald)Rational and differentCorrect answer is option 'A'. 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 roots of the equation x2 – 2 √2x + 1 = 0 area)Real and differentb)Imaginary and differentc)Real and equald)Rational and differentCorrect answer is option 'A'. Can you explain this answer?.
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