Quadratic without Linear
Let and be the two roots of the quadratic equation If the quadratic equation with the roots and has no linear term, what is the value of
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.
Since the quadratic equation with no linear term (the coefficient of x is 0) has roots ( α + k ) and ( β + k ) , then by Vieta’s formulas, we have: ( α + k ) + ( β + k ) = 0 α + β + 2 k = 0
Since α and β are the roots of 3 x 2 + 4 8 x − 7 = 0 , this implies that α + β = − 1 6 . Substituting this in α + β + 2 k = 0 , we get − 1 6 + 2 k = 0 ⇒ 2 k = 1 6 ⇒ k = 8