Let [a] denote the greatest integer less than or equal to a. given that the quadratic equation x2 + [a2 - 5a + b + 4]x +b = 0 has roots -5 and 1 , find the no. Of integral values a

DEAR FRIEND ,

ACTUALLY , NO INTEGRAL VALUE OF ‘a’ EXISTS FOR GIVEN CONDITION.

SOLUTION:-

Since , 1 is solution of given equation, on substituting 1 in place of x , you should get 0.

hence you get equation:- 

[a^2-5a+ b] +b=-5

now the  values inside the brackets are integral and when b is added ,we get integral value -5. so , b must be integral. hence we can take out b from the greatest integer brackets as it is an integer? hence , we get following equation 

[a^2-5a]+2b=-5

or .2[a^2-5a]+4b=-10                 ............equation 1.

now -5 is also solution of given equation. substituting -5 in place of x and considering b as an integer and taking it out of greatest integer brackets we get equation-

5[a^2-5a]+4b=5                   ..........equation 2.

on observation and hit and trial , we will come to conclusion that no integral value of a exists for above condition. hope you got your answer. 

FOR ANY QUERY , PLEASE ASK FREE.

THANK YOU.

Sum of roots = -4 = -[a² -5a + b +4]

ARUN,

I DON’T THINK THAT YOU HAVE ANSWERED RIGHT , BECAUSE THE QUESTION IS THAT HOW MANY INTEGRAL VALUES OF A EXIST !

BUT THE RANGE OF A YOU HAVE PROVIDED IS 

Sorry

 

And thanks Adarsh for making me correct.

Actually I think value of a is asked. But integral value of a is asked.

Hence no integral value is obtained.