[JEE Advanced 1995] if ax 2 bx c 0 has real roots alpha 1 and beta 1
If $ax^2+bx+c=0$ has real roots $\alpha<-1$ and $\beta>1$, show that $1+\frac ca+\left|\frac ba\right|<0$.
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· 2d ago
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Answer: Proved.
Dividing by $a$, $f(x)=x^2+\frac ba x+\frac ca$ has $\pm1$ between its roots, so $f(1)<0$ and $f(-1)<0$; adding gives $2(1+\frac ca)<0$ and combining yields $1+\frac ca+|\frac ba|<0$.
JEE Advanced 1995 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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