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Grade 10Algebra

The value of A for which one zero of 3x2-(1+4A)x+A2+2 may be one-third of the other is:-
(a)4
(b)33/8
(c)17/4
(d)31/8

Profile image of SAMBHAV MISHRA
7 Years agoGrade 10
Answers icon

3 Answers

Profile image of Arun
7 Years ago
Dear student
 
Let zeros are x and x/3
 
Now
 
4x/3 = (1+4A)/3
 
Also
 
x²/3 =( A²+ 2)/3
 
Now you can solve as there are two variables and two equations. I
Profile image of SAMBHAV MISHRA
7 Years ago
Hey dude I want the proper solution...
By the way,just for help ans. is 31/8
Solve it properly plz..........
Profile image of PRASHANT KUMAR JHA
ApprovedApproved Tutor Answer7 Years ago
Let the Roots be ‛p' and ‛q’ 
Thus we have q=p/3 
As it's given one root is one-third of the other. 
 
Now Sum of roots (
     p+q=(1+4A)/3
Or, p+p/3=4p/3=(1+4A)/3
 
Thus, p=(1+4A)/4 ....(eqn1)
 
Also, product of roots,
   p.q=p.p/3=(A^2+2)/3
 
Or, p^2=A^2+2
 
Now putting the value of p from eqn1
 
We have 8A=31
Thus A=31/8

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