Find the X-Intercepts of the Polynomial Function $$x ^ { 5 } - 27 x ^ { 3 } + 50 x = 0$$

question 244

Multiple Choice

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.
- $$x ^ { 5 } - 27 x ^ { 3 } + 50 x = 0$$

• A) 0 , crosses the \(x\)-axis;
• 5 , crosses the \(x\)-axis;
• \(- 5\), crosses the \(x\)-axis;
• \(\sqrt { 2 }\), crosses the \(x\)-axis;
• \(- \sqrt { 2 }\), crosses the \(x\)-axis
• B) 0 , touches the \(x\)-axis and turns around;
• 5 , crosses the \(x\)-axis;
• \(- 5\), crosses the \(x\)-axis;
• \(\sqrt { 2 }\), crosses the \(x\)-axis;
• \(- \sqrt { 2 }\), crosses the \(x\)-axis
• C) 0 , crosses the \(x\)-axis;
• 25 , touches the \(x\)-axis and turns around;
• 2 , touches the \(x\)-axis and turns around
• D) 0 , touches the \(x\)-axis and turns around;
• 25 , touches the \(x\)-axis and turns around;
• 2 , touches the \(x\)-axis and turns around

---

Definitions:

Third Party

An entity not directly involved in a transaction or legal agreement but who may be affected by it.

Force Majeure

A contractual clause that frees both parties from liability or obligation when an extraordinary event or circumstance beyond their control occurs.

Contract Termination

The legally sanctioned end of a contract's validity, which can occur due to fulfillment, mutual agreement, or breach by one of the parties.

Obligations Performance

The fulfillment or execution of the duties, actions, or tasks that are required by a contract, agreement, or legal requirement.