AP EAPCET 24-Aug-2021 Shift 1 Paper

ax2+bx+c=0 ...(i)
Let α and β are the roots of Eq. (i).
α+β=−

b

a

and αβ=

c

a

Now, the quadratic equation whose roots are

1

3α−1

,

1

3β−1

Sum of roots =

1

3α−1

+

1

3β−1

=

3β−1+3α−1

(3α−1)(3β−1)

=

3(α+β)−2

9αβ−3(α+β)+1

=

3(− b a )−2

9( c a )−3(− b a )+1

=

−3b−2a

9c+3b+a

=−

(3b+2a)

a+3b+9c

Product of roots =

1

(3α−1)(3β−1)

=

1

9αβ−3(α+β)+1

=

1

9( c a )−3(− b a )+1

=

a

a+3b+9c

Now, the required equation
x2−{−(

3b+2a

a+3b+9c

)x}+

a

a+3b+9c

=0
[∵ for any quadratic equation; . ∴ x2−( sum of roots )x+ Product of roots = 0]
⇒(a+3b+9c)x2+(3b+2a)x+a=0