BITSAT 2011 Paper

Since α and β are the roots of ax2+bx+c=0
therefore α+β=−‌

b

a

,αβ=‌

c

a

The equation ax2−bx(x−1)+c(x−1)2=0

can be written as x2(a−b+c)+(b−2c)x+c=0

Sum of the roots of this equation is


Product of the roots =‌

c

a−b+c

Thus, ax2−bx(x−1)+c(x−1)2=0
has ‌

α

a+1

,‌

β

β+1

as its two roots.