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

Question:

If a quadratic polynomial f(x) is not factorizable into linear factors, then it has no real zero. (True/False)

Solution:

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.

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now