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GiGiven that the polynomial (x2 + ax + b) leaves that same remainder when by (x – 1) or (x + 1) What are the values of a and b respectively?
- a)4 and 0
- b)0 and 3
- c)3 and 0
- d)0 and any interger
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
GiGiven that the polynomial (x2 + ax + b) leaves that same remainder w...
Since x2 + ax + b when divided by x-1 or x+1 leaves the same remainder
So on putting x=1 and x=-1 we get the same value
1+a+b = 1-a+b
2a=0
a=0
here b can take any value as it will always get cancelled out
So on putting x=1 and x=-1 we get the same value
1+a+b = 1-a+b
2a=0
a=0
here b can take any value as it will always get cancelled out
Most Upvoted Answer
GiGiven that the polynomial (x2 + ax + b) leaves that same remainder w...
To find the value of a and b, we can use polynomial long division.
When (x^2 + ax + b) is divided by (x - c), the remainder is the same as when it is divided by (x + c).
Using polynomial long division, we have:
x + c | x^2 + ax + b
| x^2 + cx
_____________
(a - c)x + b
Since the remainder is the same, we have (a - c)x + b = (a + c)x + b.
This equation holds for all values of x, so the coefficients of x on both sides must be equal:
a - c = a + c
Simplifying, we get -c = c.
This implies that c = 0.
So, when (x^2 + ax + b) is divided by (x - 0) or (x + 0), the remainder is the same.
Using polynomial long division with c = 0, we have:
x | x^2 + ax + b
| x^2
_____________
ax + b
Since the remainder is the same, we have ax + b = ax + b.
This equation holds for all values of x, so the coefficients of x on both sides must be equal:
a = a
This implies that a can be any real number.
Therefore, the values of a and b can be any real numbers.
When (x^2 + ax + b) is divided by (x - c), the remainder is the same as when it is divided by (x + c).
Using polynomial long division, we have:
x + c | x^2 + ax + b
| x^2 + cx
_____________
(a - c)x + b
Since the remainder is the same, we have (a - c)x + b = (a + c)x + b.
This equation holds for all values of x, so the coefficients of x on both sides must be equal:
a - c = a + c
Simplifying, we get -c = c.
This implies that c = 0.
So, when (x^2 + ax + b) is divided by (x - 0) or (x + 0), the remainder is the same.
Using polynomial long division with c = 0, we have:
x | x^2 + ax + b
| x^2
_____________
ax + b
Since the remainder is the same, we have ax + b = ax + b.
This equation holds for all values of x, so the coefficients of x on both sides must be equal:
a = a
This implies that a can be any real number.
Therefore, the values of a and b can be any real numbers.
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GiGiven that the polynomial (x2 + ax + b) leaves that same remainder when by (x – 1) or (x + 1) What are the values of a and b respectively?a)4 and 0b)0 and 3c)3 and 0d)0 and any intergerCorrect answer is option 'D'. Can you explain this answer?
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GiGiven that the polynomial (x2 + ax + b) leaves that same remainder when by (x – 1) or (x + 1) What are the values of a and b respectively?a)4 and 0b)0 and 3c)3 and 0d)0 and any intergerCorrect answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about GiGiven that the polynomial (x2 + ax + b) leaves that same remainder when by (x – 1) or (x + 1) What are the values of a and b respectively?a)4 and 0b)0 and 3c)3 and 0d)0 and any intergerCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for GiGiven that the polynomial (x2 + ax + b) leaves that same remainder when by (x – 1) or (x + 1) What are the values of a and b respectively?a)4 and 0b)0 and 3c)3 and 0d)0 and any intergerCorrect answer is option 'D'. Can you explain this answer?.
GiGiven that the polynomial (x2 + ax + b) leaves that same remainder when by (x – 1) or (x + 1) What are the values of a and b respectively?a)4 and 0b)0 and 3c)3 and 0d)0 and any intergerCorrect answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about GiGiven that the polynomial (x2 + ax + b) leaves that same remainder when by (x – 1) or (x + 1) What are the values of a and b respectively?a)4 and 0b)0 and 3c)3 and 0d)0 and any intergerCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for GiGiven that the polynomial (x2 + ax + b) leaves that same remainder when by (x – 1) or (x + 1) What are the values of a and b respectively?a)4 and 0b)0 and 3c)3 and 0d)0 and any intergerCorrect answer is option 'D'. Can you explain this answer?.
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