Question

the condition so that the roots of the quadratic equation ax^2 + bx + c = 0, a not equal 0, may be equal in magnitude but opposite in sign , is-​

Answer 1

Answer:

The given quadratic equation is ax

2

+bx+c=0

⇒ Let two roots be α and β.

⇒ α=−β [ Given ]

⇒ α+β−

a

−b

⇒ −β+β=

a

−−b

u

⇒ 0=

a

−b

∴ b=0 ------- ( 1 )

We have one root negative so,

∴ αβ<0

∴

a

c

<0

So, here either c or a will be negative.

Means, a and c will be having opposite sign.

a>0,c<0 or c>0,a<0 and b=0.

In options we can see option C satisfy all the conditions.

∴ Posibble conditions are a>0,b=0,c<0

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