Find a quadratic polynomial whose zeroes are - 4 and - 5 ?

To find a quadratic polynomial whose zeroes are -4 and -5, we can use the fact that if α and β are the zeroes of the quadratic polynomial, then the quadratic polynomial can be written in the form:

P(x) = a(x - α)(x - β)

Here, the zeroes are given as α = -4 and β = -5.

So, the quadratic polynomial is:

P(x) = a(x - (-4))(x - (-5)) = a(x + 4)(x + 5)

Now, expand the expression:

P(x) = a(x² + 5x + 4x + 20) = a(x² + 9x + 20)

Thus, the quadratic polynomial is:

P(x) = a(x² + 9x + 20)

If we assume a = 1 (for simplicity), the polynomial becomes:

P(x) = x² + 9x + 20

Therefore, the required quadratic polynomial is:

x² + 9x + 20