Question

If p and q are zeroes of ax^2+bx+c then find the polynomial whose zeroes are 1/p,1/q??

Answer 1

If p and q are the zeroes,

then p + q = -b/a

and pq = c/a

Now, we have to find a polynomial whose zeroes are 1/p and 1/q

p + q = -b/a

1/p + 1/q = p + q/pq

= -b/a ÷ c/a

= -b/a × a/c

= -b/c

According to this,

Alpha + Beta = -B/A

-B/A = -b/c

B = b

A = c

Also, 1/p × 1/q = 1/pq

1 ÷ c/a

= a/c

So, C/A = a/c

Again, A = c

And C = a

So, polynomial

= Ax^2 + Bx + C

= cx^2 + bx + a

Answer 2

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