A polynomial of degree 6 is graphed. It touches the x-axis at 2 distinct points and crosses it at 2 other distinct points, with no other intersections. How many real zeroes does it have counting multiplicity?

Question

Accepted Answer

6. Each touch is a double zero: 2 touches give 2 x 2 = 4. Each crossing is a single zero: 2 crossings give 2. Total counting multiplicity = 4 + 2 = 6, matching degree 6.

A polynomial of degree 6 is graphed. It touches the $x$ -axis at 2 distinct points and crosses it at 2 other distinct points, with no other intersections.
How many real zeroes does it have counting multiplicity?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Graphical Meaning of Zeroes practice

A polynomial of degree 6 is graphed. It touches the x-axis at 2 distinct points and crosses it at 2 other distinct points, with no other intersections.How many real zeroes does it have counting multiplicity?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Graphical Meaning of Zeroes practice

A polynomial of degree 6 is graphed. It touches the $x$ -axis at 2 distinct points and crosses it at 2 other distinct points, with no other intersections.
How many real zeroes does it have counting multiplicity?