Question

is -4x²+4x+1, -3x²+3x+2 a polynomial with no zeros or not

Answer 1

they are polynomials with no zeros
if we need
we get as roots they are
1)-4+√32 and -4-√32
2)-3+√33 and -3-√33

Answer 2

In -4x²+4x+1,
b^2 - 4ac = 4^2 - 4*(-4)*1 = 16+16=32 >0
Since b^2 - 4ac >0, it has two zeroes.

In -3x²+3x+2
b^2 - 4ac = 3^2 - 4*(-3)*2 = 9+24=33 >0
Since b^2 - 4ac >0, it has two zeroes.