MathDB

Let

a, b, c, r,

and

s

be real numbers. Show that if

r

is a root of ax^2\plus{}bx\plus{}c \equal{} 0 and s is a root of \minus{}ax^2\plus{}bx\plus{}c \equal{} 0, then \frac{a}{2} x^2 \plus{} bx \plus{} c \equal{} 0 has a root between

r

and

s.

77

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