Zero Product Property

What is the zero product property?

• If the product of two real numbers is zero, then at least one of the numbers must be zero.

• If the product of two real numbers is zero, then both numbers must be zero.

• If the difference of two real numbers is zero, then both numbers must be zero.

• If the sum of two real numbers is zero, then both numbers must be zero.

Tags

CCSS.HSA.REI.B.4

How is the zero product property related to quadratic equations?

• The zero product property has no relation to quadratic equations

• Quadratic equations are solved by adding the zero product to the equation

• Quadratic equations can be solved using the zero product property by setting the equation equal to zero and factoring it to find the solutions.

• Quadratic equations cannot be solved using the zero product property

Tags

CCSS.HSA.REI.B.4

If a quadratic equation can be factored into (x - 3)(x + 2) = 0, what are the solutions for x?

• x = 0, x = 1

• x = 4, x = -3

• x = 5, x = -1

• x = 3, x = -2

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

If a quadratic equation can be factored into (x + 5)(x - 4) = 0, what are the solutions for x?

• x = -5, x = 4

• x = -3, x = 2

• x = 0, x = 9

• x = 1, x = 6

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CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

Explain how the zero product property can be used to solve real-world problems involving quadratic equations.

• By using the quadratic formula to find the solutions

• By setting the equation equal to zero and factoring it to find the values of the variable that satisfy the equation.

• By dividing the equation by zero

• By adding the coefficients of the quadratic equation

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

What are the key steps to apply the zero product property to solve a quadratic equation?

• Set each factor equal to zero and solve for the variable.

• Set each factor equal to one and solve for the variable.

• Add the factors together and solve for the variable.

• Multiply the factors and solve for the variable.

Tags

CCSS.HSA.REI.B.4

Use the Zero Product Property to solve for the values of x.

 $\left(x+2\right)\left(x-3\right)=0$  

• 2 and 3

• -2 and -3

• 2 and -3

• -2 and 3

Tags

CCSS.HSA.REI.B.4

Solve using the Zero Product Property:
 $\left(3x+2\right)\left(x+1\right)=0$  

•  $x=1,\ x=\frac{2}{3}$  

•  $x=-1,\ \ x=-\frac{2}{3}$  

•  $x=2,\ x=1$  

•  $x=-1,\ \ x=\frac{2}{3}$  

Tags

CCSS.HSA.REI.B.4

What are the zeros of the function?

  $0=(2x+5)(x-6)$  

•  $x=-6,\ x=\frac{5}{2}$  

•  $x\ =-\frac{5}{2},\ x=6$  

•  $x=-5,\ x\ =\ 6$  

•  $x=5,\ x\ =-6$  

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

Solve.  

 $r\left(r+7\right)=0$  

•  $r=0,\ r=-7$  

•  $r=0,\ r=7$  

•  $r=-7$  

•  $r=7$  

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4