Question

If alpha and beta are the zeroes of the polynomial (x2 + 8x + 6) form a quadratic polynomial whose zeroes are 1/alpha and 1/beta.

Answer 1

The relation between the zeroes and coefficients of a quadratic equation are as follows:

For every polynomial of form ax²+bx+c

Now the given polynomial is

P(x) =x²+8x+6

So for this polynomial

Now,

We are asked a polynomial whose zeroes are

Now let the polynomial be f(x)

So,

For f(x) the sum of the zeroes is

Now, for the product of zeroes of f(x)

Now,

For f(x)

Sum of roots = 44/6

Product of zeroes = - 1/6

The structure of the polynomial is

K(x²-(sum of zeroes) x +(product of zeroes)

So, f(x) = k(x²-44/6-1/6)

Or, f(x) = 6x²-44x-1

When k = 6