If `a , b , c ,` are real number such that `a c!=0,` then show that at least one of the equations `a x^2+b x+c=0` and `-a x^2+b x+c=0` has real roots.

Explanation

Given `{a, b, c} in {R}`

and a c equiv 0

Let First eqn is `a x^{2}+b x+c=0`

and other is `-a x^{2}+b x+c=0`

and `D_{1} `and `D_{2}` are the discriminant of these eqn resp

Now, `={D}_{1}={b}^{2}-4 {ac}`

`{D}_{2}={b}^{2}+4 {ac}`

case i)ac <0

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