Latest TCS Aptitude Question SOLUTION: How many integers x satisfy the equation (x^2 - 4x + 5)x^2 + x = 1 3 0 more than 4 4 2

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How many integers x satisfy the equation
(x^2 - 4x + 5)x^2 + x = 1
3
0
more than 4
4
2

Asked In TCS amit shukla (10 years ago)

Unsolved Read Solution (12)

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Read Solution (12) :

RAKESH  (10 years ago)

for any values of x, the terms (x^2-4x+5) & x^2 is always positive
also x is an integer so x^2>=x
hence there is no integral soln of given equation.
ANS-0

Is this solution Helpfull? Yes (24) | No (4)  

parvez sajjad  (10 years ago)

ans=4
as x4

Is this solution Helpfull? Yes (9) | No (6)  

RAKESH  (10 years ago)

after simplification it is a 4th degree eqn so it has 4 roots
but we have to find integeral value of x,there is no integral root of eqn bcoz in eqn
(x^2 - 4x + 5)x^2 + x = 1

value of (x^2 - 4x + 5) is always +ve for any value of x
so (x^2 - 4x + 5)x^2 >0 for any x(x^2>0)
for any integer (x^2 - 4x + 5)x^2 + x never equals to 1
check for -2,-1,0,1,2 etc
hence there is no integer value of x.

Is this solution Helpfull? Yes (7) | No   

mary  (10 years ago)

(x2-4x+5)x2+x=1
x4-4x3+5x2+x-1=0
here we get a fourth order equation.therefore it has 4 roots

Is this solution Helpfull? Yes (3) | No (2)  

Amit Kumar  (10 years ago)

if x=1, LHS=3 if x=2 LHS=6 (increasing LHS for increasing x)
if x=-1 LHS=9 if x=-2 LHS=66 (increasing LHS for decreasing x)
and if x=0, LHS=0.
sol. is 0

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Priyanka Shekhaw3at  (10 years ago)

i dont get the Question and answer both guys....

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VINITA SINHA  (10 years ago)

ans= 0
since ( x^2 - 4x+ 5) has imaginary roots. so no integer will satisfy the above mentioned equation

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Akanksha Mishra  (10 years ago)

ans is 0 as no integer value is satisfying above eqn

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Prokriti Chatterjee  (10 years ago)

rakesh kumar pls explain it in details.....

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alok kumar  (10 years ago)

4 as after multiplying we get a fourth order eqn which must hav 4 roots

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Suresh kumar shaw  (10 years ago)

ans:4
becoz the highest power of x is 4 in given equation

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Umesh  (10 years ago)

f(x)= x4-4x3+5x2+x-1=0
change in sign 3 so 3 +ve real roots
again f(-x)=x4+4x3+5x2-x-1=0
change in sign =1 so 1 -ve real root so total 4 integer will satisfy the eqn
hence 4 is the ans.....
(if roots are not real they are imaginary not integers so check this out)

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