Question
If a,b,c are in Geometric Progression, then the equation ax2−2bx+c=0 and dx2−2ex+f=0 have a common root if da,eb,fc are in?
Answer: Option A
:
A
Solve it using Assumption
Put a=1,b=1,c=1.
Equation (1) is x2−2x+1=0. Sum of the roots= 2 and product of roots= 1
Thus the roots are 1,1
Let the common root be 1
Let us assume the other root =2
The equation changes to
x2+3x+2=0
Thus, 2ed=3 and fd=2
When d=1, f=2 and e=32
Thus da; eb; fc = 1, 1.5, 2 are in AP. Answer is option (a)
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:
A
Solve it using Assumption
Put a=1,b=1,c=1.
Equation (1) is x2−2x+1=0. Sum of the roots= 2 and product of roots= 1
Thus the roots are 1,1
Let the common root be 1
Let us assume the other root =2
The equation changes to
x2+3x+2=0
Thus, 2ed=3 and fd=2
When d=1, f=2 and e=32
Thus da; eb; fc = 1, 1.5, 2 are in AP. Answer is option (a)
Was this answer helpful ?
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