4EDITTED
MULTIPLE ANSWER QUESTION
If f(x) = 0 is a polynomial whose coefficents are all ± 1 and whose roots are all real, then degree of f(x) can be equal to
(A) 1 (B) 2 (C) 3 (D) 4
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17 Answers
1constant is nothing but co-efficient of 'x^{0}' in the polynomial....which i think u hav to take ±1
(Hope i m not talkink any blunder [3])
4I think there need not b a constant term becz the qs said coefficients shud be +- 1 & nothing is mentioned abt constant term
its like this
if v say an eqn has all positive coeffs then it need not be that constant term shud also be positive no???
1ya..in a general polynomial, there should be a constant term ......................which u have taken as '0'..
but qs says it should be ±1
4@Rahul (#12 )
The qs mentions that the coefficients shud be ± 1
So it is not necessary that the constant term is also ±1 na ??
@msp : I too thought the same way
@ Asish : Ya u're ans is correct
but my doubt is shud there be a constant term at all ??
106is there any mathematical proof for this??
yeah ans should be ABC
1but u have taken the constant term in the above eqn as 0,
but ques says that every term should be +1 or -1
29the eqn that u have posted can be written as x4 - 2x2 + x = 0...which do not satisfy the condition given abv...
1Uttara can u show how four??
Acc. to me, A,B,C should be right.........
29oops i misread the question ..i thought both roots and coefficients have to be ± 1 [13]
4Ya Rahul It can also be 2
In fact I was getting A B C D
But ans given is A B C
I say it can also be 4 ( Considering repeated roots)
29ya i also feel the answer shud be A and C...
logic : number of terms shud be even so that they can be cancelled out...