Location of roots of two quadratic w.r.t. to third quadratic

If such that If is a root of is a root of and then the equation has roots .

Prove that lies between

Let f(x) =

$\Rightarrow

Thus one root of will lie between

Please provide explanation on the last statement of this answer how it derived ...Thanks..

Re: Location of roots of two quadratic w.r.t. to third quadratic

Hey sachinrajsharma.

What is the definition of f(x1)(x2)? Is it in terms of f(x1) and g(x2)?

Re: Location of roots of two quadratic w.r.t. to third quadratic

implies that are opposite in sign.

Since is continuous, it must be zero at some point between and