If a quadratic polynomial f(x) is not factorizable into linear factors,

When polynomial $f(x)=a x^{2}+b x+c$ is not factorizable then the curve $y=a x^{2}+b x+c$ does not touch $x$-axis. Parabola $y=a x^{2}+b x+c$ open upwards above the $x$ axis or open downwards below $x$-axis where $a>0$ or $a<0$

Hence, if quadratic polynomial $f(x)$ is not factorizable into linear factors then it has no real zeros. True.