Find the quadratic equation ?
Such that and are roots
and geometric mean is harmonic mean is 1.5
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
The quadratic is ( x − α ) ( x − β ) = x 2 − ( α + β ) x + α β .The geometric mean is 3 = α β → α β = 3 .The harmonic mean is α 1 + β 1 2 = 2 3 → 2 α 1 + β 1 = 3 2 → α β α + β = 3 4 → 3 α + β = 3 4 → α + β = 4 .So the quadratic is x 2 − 4 x + 3