the equation formed by decreasing each root ax2+bx+c=0 by 1 is 2x2+bx+2=0 then
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SOLUTION
Let the roots of the equation
=) ax^2+ bx+c=0
be Alpha and beta
Roots of the equation
=) x^2+4x+1=0
alpha-1, Beta-1
Let y=x+1
x= y-1
The second equation becomes
=)(y-1)^2+ 4(y-1) +1=0
=) y^2-2y+1+4y-4+1=0
=) y^2-2y +1+4y-4+1=0
=) y^2 +2y -2=0
The root of the equation are
=) (alpha-1)+1= alpha and (beta-1)+1= beta
The equation in variable x is
=) x^2+2x-2=0
The equation is same as ax^2 +bx+c=0
a= 1
b= 2
c= -2
hence ,b= -c
hope it helps
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