Question

if a and 1/a are the roots of the equation px^2+qx+r then prove that p=r​

Answer 1

Product of roots = r/p
=> a x 1/a =r/p
=>r/p=1
=>r=p
Hence proved

Answer 2

Answer:

x=a and x=1/a

(x-a)=0, (x-1/a)=0

=> x-a and x-1/a are the factors of the equation

Now,

if we multiply the factors we'll get the equation

(x-a)(x-1/a)

= (x)^2+(-a-1/a)x+(-a)(-1/a)= px^2+qx+r

=x^2+(-ax-x/a)+1

=> px^2+qx+r = 1x^2+(-ax-x/a)+1

=> px^2=1x^2, p=1

=> r = 1

Thus p=r=1

p = r (proved)