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Grade 11Physical Chemistry

If α, β are the roots of the equation ax2 + bx + c = 0, then the quadratic equation whose roots are α / ( 1 + α ) and β / ( 1 + β ).

Profile image of Shubham Panchal
6 Years agoGrade 11
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1 Answer

Profile image of nandini panicker
6 Years ago
ax2+bx+c=0
sum of zeroes=-b/a =alpha+beta.....(1)
product of zeroes=c/a=alpha*beta …..(2)
given two roots = alpha/1+alpha , beta/1+beta
sum of roots=alpha+beta+2(alpha*beta)/1+alpha+beta+alpha*beta.....(3)
product of roots=alpha*beta/1+alpha+beta+alpha*beta.....(4)
putting the values from 1 and 2 into 3 and 4 we get,
sum=2a-b+2c/a-b+c
product=c/a2-ab+ac
as we know , equation should be ,x2-sx+p
eq. becomes x2-(2a-b+2c/a-b+c)x+(c/a2-ab+ac)