Verified answer

Question:

What are the solutions of (x - 3)(x - 4) = 0?

• Use the zero-product property by equating each factor to zero.

Solution:

(x - 3)(x - 4)  = 0

• x - 3 = 0
• x = 3
• x - 4 = 0
• x = 4

Answer:

• The solutions are 3 and 4.

Checking:

• (x - 3)(x - 4) = 0; x = 3, 4
• (3 - 3)(4 - 4) = 0
• (0)(4 - 4) = 0
• (0)(0) = 0
• 0 = 0 ✔

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Solve 2x(x + 5) = 0.

• By the zero-product property, equate each factor to zero to find the solution(s).

Solution:

2x(x + 5) = 0

• 2x = 0
• 2[2x = 0]2
• x = 0
• x + 5 = 0
• x = -5

Answer:

• x = 0, -5

Checking:

• 2x(x + 5) = 0; x = 0, -5
• 2(0)(-5 + 5) = 0
• 0(-5 + 5) = 0
• 0(0) = 0
• 0 = 0 ✔

Answer:

(x-3) + (x-4)=0

x+3=0 or x-4=0

x=3 or x=4

2x(x+5)=0

x=0 or x+5=0

x= -5

x=0 or x= -5