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Which of the following statements regarding quadratic equations is/are true?
(A) The quadratic equation 2x2 + ax + a = 0 has real and equal roots and the values of a are 0 and 8.
(B) The sum and the product of the roots of the equation x2 - 5x + 6 = 0 are 5 and 6, respectively.
(C) The roots 2 and - 1/2 form the equation 2x2 - 3x - 2 = 0.
- a)(A), (B) and (C)
- b)(A) and (B)
- c)(B) and (C)
- d)(C) and (A)
- e)Only (A)
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Which of the following statements regarding quadratic equations is/ar...
For (A)
For equal roots, the discriminant D of 2x2 + ax + a = 0 should be zero.
D = a2 – 4(2)(a) = 0
a2 – 8a = 0
a(a – 8) = 0
a = 0, 8.
So, (A) is correct.
For (B)
Comparing x2 - 5x + 6 = 0 and ax2 + bx + c = 0,
a = 1, b = - 5 and c = 6
Therefore,
Sum of the roots = 
= 5
= 5Product of the roots = c/α = 6/1 = 6
For (C)
The given roots are 2 and -1/2.
Therefore, sum of the roots,
And product of the given roots,
Therefore, the required equation is:
x2 – Sx + P, i.e. x2 - (sum of the roots) x + product of the roots = 0
i.e. 2x2 - 3x - 2 = 0
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Which of the following statements regarding quadratic equations is/ar...
Quadratic Equations Statements Analysis:
Statement (A):
- The quadratic equation 2x^2 + ax + a = 0 has real and equal roots if the discriminant is zero.
- The discriminant, in this case, is a^2 - 4(2)(a) = a^2 - 8a.
- Setting the discriminant to zero, we get a^2 - 8a = 0, which gives a = 0 and a = 8.
- Therefore, the values of a for real and equal roots are indeed 0 and 8.
Statement (B):
- The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is given by -b/a, and the product of the roots is given by c/a.
- For the equation x^2 - 5x + 6 = 0, the sum of the roots is 5 and the product of the roots is 6.
- Therefore, the given sum and product of the roots are 5 and 6, respectively.
Statement (C):
- For a quadratic equation of the form ax^2 + bx + c = 0, the roots are given by the formula (-b ± √(b^2 - 4ac)) / 2a.
- For the equation 2x^2 - 3x - 2 = 0, the roots are 2 and -1/2.
- Therefore, the roots given do form the equation 2x^2 - 3x - 2 = 0.
Conclusion:
- Statement (A), (B), and (C) are all true based on the analysis of the given quadratic equations.
- Hence, option (a) is the correct answer as all the statements are true.
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Which of the following statements regarding quadratic equations is/are true?(A) The quadratic equation 2x2 + ax + a = 0 has real and equal roots and the values of a are 0 and 8.(B) The sum and the product of the roots of the equation x2 - 5x + 6 = 0 are 5 and 6, respectively.(C) The roots 2 and - 1/2 form the equation 2x2 - 3x - 2 = 0.a)(A), (B) and (C)b)(A) and (B)c)(B) and (C)d)(C) and (A)e)Only (A)Correct answer is option 'A'. Can you explain this answer?
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Which of the following statements regarding quadratic equations is/are true?(A) The quadratic equation 2x2 + ax + a = 0 has real and equal roots and the values of a are 0 and 8.(B) The sum and the product of the roots of the equation x2 - 5x + 6 = 0 are 5 and 6, respectively.(C) The roots 2 and - 1/2 form the equation 2x2 - 3x - 2 = 0.a)(A), (B) and (C)b)(A) and (B)c)(B) and (C)d)(C) and (A)e)Only (A)Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Which of the following statements regarding quadratic equations is/are true?(A) The quadratic equation 2x2 + ax + a = 0 has real and equal roots and the values of a are 0 and 8.(B) The sum and the product of the roots of the equation x2 - 5x + 6 = 0 are 5 and 6, respectively.(C) The roots 2 and - 1/2 form the equation 2x2 - 3x - 2 = 0.a)(A), (B) and (C)b)(A) and (B)c)(B) and (C)d)(C) and (A)e)Only (A)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements regarding quadratic equations is/are true?(A) The quadratic equation 2x2 + ax + a = 0 has real and equal roots and the values of a are 0 and 8.(B) The sum and the product of the roots of the equation x2 - 5x + 6 = 0 are 5 and 6, respectively.(C) The roots 2 and - 1/2 form the equation 2x2 - 3x - 2 = 0.a)(A), (B) and (C)b)(A) and (B)c)(B) and (C)d)(C) and (A)e)Only (A)Correct answer is option 'A'. Can you explain this answer?.
Which of the following statements regarding quadratic equations is/are true?(A) The quadratic equation 2x2 + ax + a = 0 has real and equal roots and the values of a are 0 and 8.(B) The sum and the product of the roots of the equation x2 - 5x + 6 = 0 are 5 and 6, respectively.(C) The roots 2 and - 1/2 form the equation 2x2 - 3x - 2 = 0.a)(A), (B) and (C)b)(A) and (B)c)(B) and (C)d)(C) and (A)e)Only (A)Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Which of the following statements regarding quadratic equations is/are true?(A) The quadratic equation 2x2 + ax + a = 0 has real and equal roots and the values of a are 0 and 8.(B) The sum and the product of the roots of the equation x2 - 5x + 6 = 0 are 5 and 6, respectively.(C) The roots 2 and - 1/2 form the equation 2x2 - 3x - 2 = 0.a)(A), (B) and (C)b)(A) and (B)c)(B) and (C)d)(C) and (A)e)Only (A)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements regarding quadratic equations is/are true?(A) The quadratic equation 2x2 + ax + a = 0 has real and equal roots and the values of a are 0 and 8.(B) The sum and the product of the roots of the equation x2 - 5x + 6 = 0 are 5 and 6, respectively.(C) The roots 2 and - 1/2 form the equation 2x2 - 3x - 2 = 0.a)(A), (B) and (C)b)(A) and (B)c)(B) and (C)d)(C) and (A)e)Only (A)Correct answer is option 'A'. Can you explain this answer?.
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