Arjun argues: 'If a polynomial graph stays strictly above the x-axis except where it just touches it once, the polynomial must have even degree.' Which reasoning best supports this for the simplest case?

Question

Accepted Answer

Both arms point the same way (upward), which happens for even degree; the single touch is a repeated zero. If the curve stays above the x-axis on both far sides, both ends rise, which is characteristic of even-degree polynomials (e.g. a parabola), and the single touch represents a repeated zero.

Arjun argues: 'If a polynomial graph stays strictly above the $x$ -axis except where it just touches it once, the polynomial must have even degree.'
Which reasoning best supports this for the simplest case?

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More Class 10 Graphical Meaning of Zeroes practice

Arjun argues: 'If a polynomial graph stays strictly above the x-axis except where it just touches it once, the polynomial must have even degree.'Which reasoning best supports this for the simplest case?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Graphical Meaning of Zeroes practice

Arjun argues: 'If a polynomial graph stays strictly above the $x$ -axis except where it just touches it once, the polynomial must have even degree.'
Which reasoning best supports this for the simplest case?