13Thnx bhaiyaa[1]
fr 2) Bhaiya, it was an integer type Qn, so i think,
if a=89/11 , they are asking us this value= (89+11) which is correctly 100 as per the given answer.
Doubts...
1) If the equation x4 -(3m+2)x2 +m2=0 (m>0), has 4 real solutions which are in A.P., find the value of "m".
2) Let P(x) be a Polynomial of degree 4 such tht -
P(1)=P(3)=P(5)=P'(7) =0.
If the real number x (≠1,3,5) is such tht P(x)=0 can be expressed as x=u/v (u & v being relatively prime), what is the value of (u+v) ?
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3 Answers
62if a is a roo tto the first one, -a is also a root
so the roots of the above if real are : -3a, -a, a, 3a (for real roots to be in AP)
hence 9a4=m4 => 3a2=±m2
and -9a2-a2=-3m-2 =>10a2=3m+2
so m2-3m-2=0 so m = 3±√9+82 = 3±√172
or m2+3m+2=0 so m=-1 or -2
There is only one +ve root above...
622) Let P(x) be a Polynomial of degree 4 such tht -
P(1)=P(3)=P(5)=P'(7) =0.
If the real number x (≠1,3,5) is such tht P(x)=0 can be expressed as x=u/v (u & v being relatively prime), what is the value of (u+v) ?
P(x) = (x-1)(x-3)(x-5)(x-a)
P'(x) =(x-1)(x-3)(x-5)(x-a)[1/(x-1)+1/(x-3)+1/(x-5)+1/(x-a)] at x=7 , it is zero...
hence 0=1/6+1/4+1/2+1/(7-a)
so 1/(a-7) = 11/12
so a=8+1/11 = 89/11
From here, i did not understand what is meant by this last step.. if P(x) can be expressed as u/v.. because all rational numbers can be!
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