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