If the equations, have a common root then which of the following options might be true?
Select one or more
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.
Let us write the factored forms of each quadratic equation:
x 2 + a x + b = ( x − α ) ( x − α b ) = 0
x 2 + b x + a = ( x − α ) ( x − α a ) = 0
By Vieta's Formula, we now obtain the following coefficient relationships:
α + α b = − a (i)
α + α a = − b (ii)
Subtracting (ii) from (i) will produce α b − a = b − a ⇒ α = 1 . Substituting this value back into either (i) or (ii) produces a + b + 1 = 0 . Hence, choice 3 is correct.