CDS Model Paper 3 Mathematics

ax2+bx+b=0
⇒ x2+

b

a

x+

b

a

=0
∴ Sum of roots, α+β=

−b

a

and Products of roots, αβ=

b

a

Hence, product of roots is not equal to the sum of roots, so Statement I not correct.
Now, for roots to be real and uequal.
∴ Determinant, D>0
⇒ b2−4ac>0
⇒ b2−4a(b)>0
⇒ b2−4ab>0
⇒ b2>4ab
∴ b>4a
So, if b>4a, then roots are unequal and real, so Statement II is not always true it will depend on values of a and b.