Class 10 Exam > Class 10 Questions > If A and B are the roots of the quadratic equ...
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If A and B are the roots of the quadratic equation x2 - 12x + 27 = 0, then A3 + B3 is
- a)27
- b)729
- c)756
- d)64
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If A and B are the roots of the quadratic equation x2 - 12x + 27 = 0, ...
Given:
The quadratic equation is x^2 - 12x + 27 = 0
To find:
The value of A^3 + B^3
Solution:
We know that if A and B are the roots of a quadratic equation ax^2 + bx + c = 0, then the sum of the roots is given by A + B = -b/a and the product of the roots is given by AB = c/a.
So, in the given equation x^2 - 12x + 27 = 0, the sum of the roots A and B is A + B = 12 and the product of the roots A and B is AB = 27.
Now, let's find the value of (A^3 + B^3).
Step 1:
We know that (A + B)^3 = A^3 + B^3 + 3AB(A + B)
Substituting the given values, (A + B)^3 = (12)^3
Simplifying, (A + B)^3 = 1728
Step 2:
Expanding (A + B)^3, we get A^3 + 3A^2B + 3AB^2 + B^3 = 1728
Step 3:
Substituting the values of AB and simplifying, we get A^3 + B^3 + 3(27)(12) + 12(3)(27) = 1728
Simplifying further, we get A^3 + B^3 + 324 + 972 = 1728
Step 4:
Combining like terms, we get A^3 + B^3 + 1296 = 1728
Step 5:
Subtracting 1296 from both sides, we get A^3 + B^3 = 1728 - 1296
Simplifying, we get A^3 + B^3 = 432
Answer:
Therefore, the value of A^3 + B^3 is 432.
The quadratic equation is x^2 - 12x + 27 = 0
To find:
The value of A^3 + B^3
Solution:
We know that if A and B are the roots of a quadratic equation ax^2 + bx + c = 0, then the sum of the roots is given by A + B = -b/a and the product of the roots is given by AB = c/a.
So, in the given equation x^2 - 12x + 27 = 0, the sum of the roots A and B is A + B = 12 and the product of the roots A and B is AB = 27.
Now, let's find the value of (A^3 + B^3).
Step 1:
We know that (A + B)^3 = A^3 + B^3 + 3AB(A + B)
Substituting the given values, (A + B)^3 = (12)^3
Simplifying, (A + B)^3 = 1728
Step 2:
Expanding (A + B)^3, we get A^3 + 3A^2B + 3AB^2 + B^3 = 1728
Step 3:
Substituting the values of AB and simplifying, we get A^3 + B^3 + 3(27)(12) + 12(3)(27) = 1728
Simplifying further, we get A^3 + B^3 + 324 + 972 = 1728
Step 4:
Combining like terms, we get A^3 + B^3 + 1296 = 1728
Step 5:
Subtracting 1296 from both sides, we get A^3 + B^3 = 1728 - 1296
Simplifying, we get A^3 + B^3 = 432
Answer:
Therefore, the value of A^3 + B^3 is 432.
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Community Answer
If A and B are the roots of the quadratic equation x2 - 12x + 27 = 0, ...
Given A and B are the roots of x2 - 12x + 27 = 0
⇒ (x - 3)(x - 9) = 0
∴ A = 3, B = 9
Hence A3 + B3 = 33 + 93 = 27 + 729 = 756
⇒ (x - 3)(x - 9) = 0
∴ A = 3, B = 9
Hence A3 + B3 = 33 + 93 = 27 + 729 = 756
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If A and B are the roots of the quadratic equation x2 - 12x + 27 = 0, then A3 + B3 isa)27b)729c)756d)64Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If A and B are the roots of the quadratic equation x2 - 12x + 27 = 0, then A3 + B3 isa)27b)729c)756d)64Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are the roots of the quadratic equation x2 - 12x + 27 = 0, then A3 + B3 isa)27b)729c)756d)64Correct answer is option 'C'. Can you explain this answer?.
If A and B are the roots of the quadratic equation x2 - 12x + 27 = 0, then A3 + B3 isa)27b)729c)756d)64Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If A and B are the roots of the quadratic equation x2 - 12x + 27 = 0, then A3 + B3 isa)27b)729c)756d)64Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are the roots of the quadratic equation x2 - 12x + 27 = 0, then A3 + B3 isa)27b)729c)756d)64Correct answer is option 'C'. Can you explain this answer?.
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