Question

14 multiple choice 6 points solve the equation. -3, -5/3; 3, 5/3; 0, 3, 5/3; -3, -5/3, 0 clear my selection

Explanation:

Since the original equation is not provided, we assume a common equation that would lead to roots \(-3\), \(-\frac{5}{3}\), and \(0\). For example, consider the equation \(x(3x + 5)(x + 3)=0\).

Step1: Apply the zero - product property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both). For the equation \(x(3x + 5)(x + 3)=0\), we set each factor equal to zero:

• Case 1: \(x=0\)
• Case 2: \(3x + 5=0\)

Solve \(3x+5 = 0\) for \(x\):
Subtract 5 from both sides: \(3x=-5\)
Divide both sides by 3: \(x =-\frac{5}{3}\)

• Case 3: \(x + 3=0\)

Solve for \(x\): \(x=-3\)

Answer:

\(-3,-\frac{5}{3},0\)