find the polynomial whose zeroes are -5 and -4.
To find the polynomial whose zeroes are -5 and -4, we can use the fact that if a number, say 'a', is a zero of a polynomial, then (x - a) is a factor of that polynomial.
So, if -5 and -4 are the zeroes of a polynomial, we can write the factors as (x - (-5)) and (x - (-4)), which simplifies to (x + 5) and (x + 4).
To find the polynomial, we multiply these factors together:
(x + 5)(x + 4)
Expanding this expression gives:
x² + 4x + 5x + 20
Combining like terms yields the polynomial:
x² + 9x + 20
Therefore, the polynomial with zeroes -5 and -4 is x² + 9x + 20.
if zeroes are -5 and -4
we have factors of (x+5) and (x+4)
the polynomial is
(x+5)(x+4)
expand if needed