Question

Find a quadratic polynomial the sum and product of zeros are 0and -root 2 respectively

Answer 1

The sum of the zeroes = 0

The product of the Zeroes = - root2

The general form of a quadratic polynomial is as follows :-

K(x² - (sum) x + product)

Where the sum and product are of the two zeroes of the polynomial.

Now,

We have both sum as well as product of the zeroes..

Thus,

Putting down the values in the formula :-

We get :-

K(x² - 0x + (-root2))

There can be infinite polynomial with this sum and product.

The polynomial can be:-

x² - root2

Or

Root2 x² - 2

And so on!