Question

4.Mrs. Collins is at the table with you and states that the fourth-degree graphs she has seen have four real zeros. She asks you if it is possible to create a fourth-degree polynomial with only two real zeros. Demonstrate how to do this and explain your steps.

Answer 1

You can create a fourth degree polynomial with only two real zeros. The other two can be complex zeros.

Answer 2

Start with a quadratic function: ax^2 + bx + c.
A quadratic function will have complex roots when the discriminant is negative. Discriminant is b^2 - 4ac
Choose suitable values for a, b and c such that b^2 - 4ac < 0.
Then the quadratic equation will have two complex roots.

Then take another quadratic that has two real roots.
For example, (x - 1)(x - 2) is a quadratic with two real roots: 1 and 2.

Multiply the first and the second quadratic and you will have a fourth degree polynomial with two real roots and two complex roots.

Answer 3

Thank you so much for your help!

Answer 4

you are welcome.