Question

The quadratic polynomial x^2 +mx+n has roots twice those of x^2 +px+m, and none of m,n, and p is zero. What is the value of n/p?

Answer 1

n/p = 8.

Explanation:

If the roots of the first equation are A and B we have

A + B = -m and AB = n.

This has roots twice the roots of the second equation so we have:

0.5(A + B) = -p and 0.25AB = m.

So A + B = -2p and AB = 4m

Equating values of A +B and AB:

-m = -2p and n = 4m

m = 2p and m = n/4

2p = n/4

n = 8p

n/p = 8.