Problem

For both roots to be less than 1, you need three conditions to work together: the parabola must open upward (✓ already true), it must have real roots, and its vertex must lie to the left of $x = 1$ while the function value at $x = 1$ stays positive. The key insight is that if both roots are smaller than 1, then $f(1) > 0$ acts as a boundary check, and the axis of symmetry (which is the average of the roots) must also be less than 1.

For both roots to be less than 1, you need three conditions to work together: the parabola must open upward (✓ already true), it must have real roots, and its vertex must lie to the left of $x = 1$ while the function value at $x = 1$ stays positive. The key insight is that if both roots are smaller than 1, then $f(1) > 0$ acts as a boundary check, and the axis of symmetry (which is the average of the roots) must also be less than 1.