Question

Find the condition that
(1) one of the roots of the equation ax2+bx+c = 0 may be unity.
(ii) one of the roots of the equation ax2 + bx + c = 0 may be zero.
(ii) exactly one of the roots of the equation ax2 + bx + c = 0 may be zero.
(iv) both the roots of the equation ax2 + bx + c = 0 may be zero.
(U) one of the roots of the equation ax2 + bx + c = 0 may be positive and the other
negative.
of the roots of the equation​

Answer 1

Step-by-step explanation:

ANSWER

Let α and β be the roots of the following equation.

It is given that α=2β

α+β=3β=−

a

b

...(i)

αβ=2β

2

=

a

c

...(ii)

Therefore (

9a

2

b

2

)=

2a

c

⇒2b

2

=9ac