Question

If A.M. and G.M. of roots of a quadratic equation are 10 and 4, respectively, then obtain the quadratic equation.

Answer 1

ANSWER

Let a and b be the roots the quadratic equation.

Then,the quadratic equation is

x

2

−(a+b)x+ab=0..........(i)

It is given that AM=8 and GM=5.

i.e.

2

a+b

=8 and

ab

=5⇒a+b=16 and ab=25

Substituting these values in (i),we obtain x

2

−16x+25=0 as the required equation.