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If the polynomials 2x3 + mx2 +3x – 5 and x3 + x2 – 4x + m leaves the same remainder when divided by x – 2, then the value of m is
- a)-(3/13)
- b)-(13/3)
- c)3/13
- d)13/3
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If the polynomials 2x3 + mx2 +3x – 5 and x3 + x2 – 4x + m ...
Let p(x) = 2x3 + mx2 + 3x – 5 and q(x) = x3 + x2 – 4x + m.
By remainder theorem, the remainders are p(2) and q(2)
But p(2) = q(2) (given)
2(2)3 + m(2)2 + 3(2) – 5 = (2)3 + (2)2 – 4(2) + m
⇒ 16 + 4m + 6 – 5 = 8 + 4 – 8 + m
⇒ 17 + 4m = 4 + m
⇒ 3m = –13
⇒ m = – (13/3)
By remainder theorem, the remainders are p(2) and q(2)
But p(2) = q(2) (given)
2(2)3 + m(2)2 + 3(2) – 5 = (2)3 + (2)2 – 4(2) + m
⇒ 16 + 4m + 6 – 5 = 8 + 4 – 8 + m
⇒ 17 + 4m = 4 + m
⇒ 3m = –13
⇒ m = – (13/3)
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If the polynomials 2x3 + mx2 +3x – 5 and x3 + x2 – 4x + m leaves the same remainder when divided by x – 2, then the value of m isa)-(3/13)b)-(13/3)c)3/13d)13/3Correct answer is option 'B'. Can you explain this answer?
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