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Grade 11Algebra

If roots of two equations are in AP find ratio of their discriminants

Bhavana

10 Years agoGrade 11

1 Answer

BALAJI ANDALAMALA

10 Years ago

Let a,b and c,d are the roots of the two equations.
The equatios are
$x^2-(a+b)x+ab=0\,\,and\,\,x^2-(c+d)x+cd=0$

With discriminants D1 and D2.

$D_1 = (a+b)^2-4ab = (a-b)^2$
$D_2 = (c+d)^2-4cd = (c-d)^2$
Given a,b,c,d are in A.P , So b-a = d-c

$\therefore \frac{D_1}{D_2} = \frac{(a-b)^2}{(c-d)^2} = 1$

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