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Read the given statements carefully and state 'T' for true and 'F' for false.
(i) The roots of the quadratic equation ax² + bx + c = 0 are given by (-b ± √(b²-4ac)) / 2a.
(ii) The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.
(iii) If the discriminant is negative, the quadratic equation has two real and distinct roots.
(i) The roots of the quadratic equation ax² + bx + c = 0 are given by (-b ± √(b²-4ac)) / 2a.
(ii) The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.
(iii) If the discriminant is negative, the quadratic equation has two real and distinct roots.
- a)(i)-T, (ii)-T, (iii)-F
- b)(i)-F, (ii)-T, (iii)-T
- c)(i)-T, (ii)-F, (iii)-T
- d)(i)-T, (ii)-T, (iii)-T
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Read the given statements carefully and state T for true and F for fal...
(i) The roots of the quadratic equation ax² + bx + c = 0 are indeed given by (-b ± √(b²-4ac)) / 2a, which is correct.
(ii) The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac, which is also correct.
(iii) If the discriminant is negative, the quadratic equation has two complex conjugate roots, not two real and distinct roots, which makes this statement false.
(ii) The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac, which is also correct.
(iii) If the discriminant is negative, the quadratic equation has two complex conjugate roots, not two real and distinct roots, which makes this statement false.
Most Upvoted Answer
Read the given statements carefully and state T for true and F for fal...
Understanding the Statements
The question examines three statements related to quadratic equations, specifically of the form ax² + bx + c = 0. Let's analyze each statement to understand why option 'A' is the correct answer.
Statement (i):
- The roots of the quadratic equation ax² + bx + c = 0 are given by the formula (-b ± √(b² - 4ac)) / 2a.
- This statement is True (T). This is the standard formula known as the quadratic formula, used to find the roots of a quadratic equation.
Statement (ii):
- The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.
- This statement is also True (T). The discriminant helps determine the nature of the roots of the quadratic equation.
Statement (iii):
- If the discriminant is negative, the quadratic equation has two real and distinct roots.
- This statement is False (F). When the discriminant is negative, it indicates that the quadratic equation has no real roots; instead, it has two complex roots.
Conclusion
Based on the analysis:
- Statement (i) is True (T).
- Statement (ii) is True (T).
- Statement (iii) is False (F).
Thus, the correct answer is option 'A', which states: (i)-T, (ii)-T, (iii)-F. This indicates a clear understanding of the properties of quadratic equations and their discriminants.
The question examines three statements related to quadratic equations, specifically of the form ax² + bx + c = 0. Let's analyze each statement to understand why option 'A' is the correct answer.
Statement (i):
- The roots of the quadratic equation ax² + bx + c = 0 are given by the formula (-b ± √(b² - 4ac)) / 2a.
- This statement is True (T). This is the standard formula known as the quadratic formula, used to find the roots of a quadratic equation.
Statement (ii):
- The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.
- This statement is also True (T). The discriminant helps determine the nature of the roots of the quadratic equation.
Statement (iii):
- If the discriminant is negative, the quadratic equation has two real and distinct roots.
- This statement is False (F). When the discriminant is negative, it indicates that the quadratic equation has no real roots; instead, it has two complex roots.
Conclusion
Based on the analysis:
- Statement (i) is True (T).
- Statement (ii) is True (T).
- Statement (iii) is False (F).
Thus, the correct answer is option 'A', which states: (i)-T, (ii)-T, (iii)-F. This indicates a clear understanding of the properties of quadratic equations and their discriminants.
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Question Description
Read the given statements carefully and state T for true and F for false.(i) The roots of the quadratic equation ax² + bx + c = 0 are given by (-b ± √(b²-4ac)) / 2a.(ii) The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.(iii) If the discriminant is negative, the quadratic equation has two real and distinct roots.a)(i)-T, (ii)-T, (iii)-Fb)(i)-F, (ii)-T, (iii)-Tc)(i)-T, (ii)-F, (iii)-Td)(i)-T, (ii)-T, (iii)-TCorrect answer is option 'A'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Read the given statements carefully and state T for true and F for false.(i) The roots of the quadratic equation ax² + bx + c = 0 are given by (-b ± √(b²-4ac)) / 2a.(ii) The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.(iii) If the discriminant is negative, the quadratic equation has two real and distinct roots.a)(i)-T, (ii)-T, (iii)-Fb)(i)-F, (ii)-T, (iii)-Tc)(i)-T, (ii)-F, (iii)-Td)(i)-T, (ii)-T, (iii)-TCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Read the given statements carefully and state T for true and F for false.(i) The roots of the quadratic equation ax² + bx + c = 0 are given by (-b ± √(b²-4ac)) / 2a.(ii) The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.(iii) If the discriminant is negative, the quadratic equation has two real and distinct roots.a)(i)-T, (ii)-T, (iii)-Fb)(i)-F, (ii)-T, (iii)-Tc)(i)-T, (ii)-F, (iii)-Td)(i)-T, (ii)-T, (iii)-TCorrect answer is option 'A'. Can you explain this answer?.
Read the given statements carefully and state T for true and F for false.(i) The roots of the quadratic equation ax² + bx + c = 0 are given by (-b ± √(b²-4ac)) / 2a.(ii) The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.(iii) If the discriminant is negative, the quadratic equation has two real and distinct roots.a)(i)-T, (ii)-T, (iii)-Fb)(i)-F, (ii)-T, (iii)-Tc)(i)-T, (ii)-F, (iii)-Td)(i)-T, (ii)-T, (iii)-TCorrect answer is option 'A'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Read the given statements carefully and state T for true and F for false.(i) The roots of the quadratic equation ax² + bx + c = 0 are given by (-b ± √(b²-4ac)) / 2a.(ii) The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.(iii) If the discriminant is negative, the quadratic equation has two real and distinct roots.a)(i)-T, (ii)-T, (iii)-Fb)(i)-F, (ii)-T, (iii)-Tc)(i)-T, (ii)-F, (iii)-Td)(i)-T, (ii)-T, (iii)-TCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Read the given statements carefully and state T for true and F for false.(i) The roots of the quadratic equation ax² + bx + c = 0 are given by (-b ± √(b²-4ac)) / 2a.(ii) The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.(iii) If the discriminant is negative, the quadratic equation has two real and distinct roots.a)(i)-T, (ii)-T, (iii)-Fb)(i)-F, (ii)-T, (iii)-Tc)(i)-T, (ii)-F, (iii)-Td)(i)-T, (ii)-T, (iii)-TCorrect answer is option 'A'. Can you explain this answer?.
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