# Lesson Worksheet: Roots of Cubic Functions Mathematics

In this worksheet, we will practice finding the roots of cubic functions with integer coefficients.

**Q3: **

Find the value of , given the set contains the zero of the function .

**Q5: **

Solve the equation .

- A, ,
- B, ,
- C, ,
- D, ,
- E, ,

**Q6: **

Determine the solution set of the equation in .

- A
- B
- C
- D
- E

**Q7: **

Solve .

- A
- B
- C
- D or
- E or

**Q8: **

Solve .

- A
- B or
- C
- D
- E or

**Q9: **

Find the solution set of in .

- A
- B
- C
- D
- E

**Q15: **

The figure shows the curve together with the line which has slope and passes through point .

Write a cubic polynomial whose roots are , , and 1.

- A
- B
- C
- D
- E

Divide this polynomial by to get a quadratic that is a multiple of .

- A
- B
- C
- D
- E

Since , determine in terms of .

- A
- B
- C
- D
- E

Imagine changing the value of the slope so that the value of gets closer and closer to 1. When , the line will be tangent to the curve at the point . Determine the equation of the tangent to the curve at the point .

- A
- B
- C
- D
- E

**Q16: **

Liam has listed what he thinks are the possible types of real roots for a cubic function:

- One real root,
- Three equal real roots,
- Three real roots where two are equal and one is distinct,
- Three distinct real roots.

Sophia says that itβs possible to have exactly two real roots, which are distinct. Is Sophia correct?

- AYes
- BNo