If the roots of a x2 + b x + c =0 are equal in magnitude but opposite in sign, then --------------.
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Step-by-step explanation:
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
⇒ 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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