Question

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

Answer 1

This statement is true.

Explanation:

When polynomial `f(x) = ax^2 + bx + c` is not factorizable then the curve `y = ax^2 + bx + c` does not touch x-axis. Parabola  `y = ax^2 + bx + 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.