CDS Model Paper 1 Mathematics

For the given equation ax2+bx+c=0,m and n are the roots
∴ Sum of roots =m+n=−

b

a

and Product of roots =mn=

c

a

Sum of roots \& of required equation =

m2+1

m

andn2+1n
=

m2+1

m

+

n2+1

n

=

m2n+n+mn2+m

mn

=

mn(m+n)+(m+n)

mn

=

(m+n)(mn+1)

mn

=

− b a ( c a +1)

c a

=

−b(a+c)

ac

Put m+n=−

b

a

and mn=

c

a

∴ Product of roots =

m2+1

m

×

n2+1

n

=

(m2+1)(n2+1)

mn

=

m2n2+n2+m2+1

mn

=

(mn)2+(m+n)2−2mn+1

mn

=

( c a )2+( −b a )2−2( c a )+1

c a

=

c2+b2−2ac+a2

ac

=

b2+(a−c)2

ac

We know that, quadratic equation is of the form x2− (Sum of roots) x+ Product of roots =0
⇒ x2−(

−b(a+c)

ac

)x+(

b2+(a−c)2

ac

)=0
⇒ acx2+b(a+c)x+b2+(a−c)2=0
⇒ acx2+(ab+bc)x+b2+(a−c)2=0