Question

If the roots of a quaadratic equation are equal in magnitude and opposite in sign then find the value

of cofficient of x.

please answer correctly......​

Answer 1

$\huge\sf{Solution:- }$

Let ,The given quadratic equation is $\sf ax^2+bx+c=0$

⇒ Let two roots be α and β.

⇒ $\sf α=−β$ [ Given ]

⇒ $\sf α+β−\dfrac{-b}{a}$

⇒ $\sf −β+β=\dfrac{--b}{a}$

⇒ $\sf 0=\dfrac{-b}{a}$

∴ $\sf b=0$ ------- ( 1 )

We have one root negative so,

∴ $\sf αβ<0$

∴ $\sf \dfrac{c}{a}<0$

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.

so,cofficient of x=0