The value of (x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)(x-8)(x-9)(x-10) at x = 0.5, 1.5, 2.5, 3.5, 4.5, 5.5

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25 Apr 2012 sign

The value of (x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)(x-8)(x-9)(x-10) at x = 0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5 are

OPtion

1) 4 positive, 6 negative values
2) 5 positive, 5 negative values
3) 4 positive, 5 negative and one zero value
4) all positive values
5) 8 positive, 2 negative values
6) 6 positive, 4 negative values
7) all negative values
8) all zeros
9) 9 positive and 1 negative
10)none of these

Solution

it will be + for 0.5 and - for 1.5 then it will be alternatively +, -
so 5 + ND 5 -

Correct Option: 2 Best Solution (12)

B.Senthil Kumar   12 years AGO

x=0.5 result is +ve
x=1.5 result is -ve
x=2.5 result is +ve
x=3.5 result is -ve
x=4.5 result is +ve
x=5.5 result is -ve
x=6.5 result is +ve
x=7.5 result is -ve
x=8.5 result is +ve
x=9.5 result is -ve

Like? Yes (4) | No   

chiru   12 years AGO

for 0.5,2.5,4.5,6.5,8.5 all are +ve values
for 1.5,3.5,5.5,7.5,9.5 all are -ve values
hence option 2 is the answer

Like? Yes (2) | No   

Devendra Marghade   12 years AGO

the value of root of x are the products that gives the alternate +ve and -ve values.

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shyoram Gurjar   12 years AGO

-ve for1.5,3.5,5.5,7.5,9.5
+ve for0.5,2.5,4.5,6.5,8.5

Hence 5 positive and 5 negative option 2

Like? Yes (1) | No   

niru   12 years AGO

if we put x=0.5 then there will value of positive
if we put x=1.5 then there will negaitive value
then there will alternate positive and negative value ..............therefore there will 5 psitive and 5 negative value

Like? Yes (2) | No (1)  

prithviraj sanningannavar   12 years AGO

for x={0.5,2.5,4.5,6.5,8.5} we get positive values and for other values of x we get negative values so option 2 is the answer.

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Flower   12 years AGO

(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)(x-8)(x-9)(x-10)
0.5 = 639383.8623
1.5 = -33651.78223
2.5 = 5938.549805
3.5 = -1979.516602
4.5 = 1065.893555
5.5 = -872.0947266
6.5 = 1065.893555
7.5 = -1979.516602
8.5 = 5938.549805
9.5 = -33651.78223

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prem kumar.s   12 years AGO

x=0.5 we apply got it passitive values
x=1.5 we apply got it negative values

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Balakumaran N.A   12 years AGO

5 positive and 5 negative values...

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Rakesh Kumar Kohli   12 years AGO

When x=0.5 , all 10 terms in product are -ve giving product positive.
When x=1.5 , 9 terms in product are -ve giving product negative.
When x=2.5 , 8 terms in product are -ve giving product positive.
When x=3.5 , 7 terms in product are -ve giving product negative.
When x=4.5 , 6 terms in product are -ve giving product positive.
When x=5.5 , 5 terms in product are -ve giving product negative.
When x=6.5 , 4 terms in product are -ve giving product positive.
When x=7.5 , 3 terms in product are -ve giving product negaitive.
When x=8.5 , 2 terms in product are -ve giving product positive.
When x=9.5 , 1 term in product is -ve giving product negative.

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Karan Babbar   12 years AGO

Putting x=0.5, we get all (-) ve values n since values r even so overall answer is a positive interger.

Putting x=1.5, we get 1 positive n all (-) values, thereby a negative integer

Similarly going on values on odd side (1,3,5,7,9) gives u a positive numbers n d one on negative side gives u a negative no, thereby making 4 positive n 5 negative numbers

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amrit bhagat   12 years AGO

if we put 0.5 in the equation we will get 10 negative numbers and multiplying all we will postive number.
if we put 1.5 in the equation we will get 9 negative number and one postive number and multiplying all we will get neagtive number
and so on....

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