Question

nif (.b) is a root of the quadratic equation X2+bx+1-b=0 then find the roots of the equation
ted to if (1-b) is a root of the quadratic equation X^2+bx+1-b=0 then find the roots of the equation​

Answer 1

given

b is a root of equation x²+bx+1-b= 0

solution

since b is root then substituting x=b in equation it must be zero

b²+bb+1-b=0

2b²-b+1= 0

b= [1±√ (1- 4×2×1) ] / 2×2

=( 1±√-7) / 4

therefore one root= (1+√-7)/4

second root= (1+√-7)/4

similarly if 1-b is a root then put x= 1-b in eqn

(1-b)²+b(1-b)+1-b=0

1+b²-2b-b-b²+1-b= 0

-4b+2=0

4b= 2

b= 1/2

therefore both roots are equal= 1/2