Question

the equation formed by decreasing each root ax2+bx+c=0 by 1 is 2x2+bx+2=0 then​

Answer 1

here is your answer in the pic:

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Answer 2

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