Zero Product Property - Definition & Examples
Read this topicExplanations 4
- (Video) Zero Property by GVSUmath This video by GVSUmath explains the zero product property. Summary\large{\text{Summary}}Summary The zero product property states: A⋅B=0A \cdot …
By Stefan Cuevas, Alex Federspiel, Ruiran Xun, Liza Sulkin, Evan Fang, Amy Feraco, Jonathan Heller, Dani, Anusha Rahman
- The zero product property tells us that if the product of any number of expressions is zero, at least one of them must be zero: a⋅b⋅c=0 means that a=0 or b=0 or c=0a\cdot b\cdot…
By Hannah Bonville, Alex Federspiel, Liza Sulkin, Joshua Siktar, Jonathan Heller, Dani, Anusha Rahman
- The zero-product property is what allows us to find the zeroes of a polynomial by factoring it. Consider the expression a⋅b=0.a\cdot b = 0.a⋅b=0. Intuitively it makes sense that…
By Ruiran Xun, Alex Federspiel
- Zero Product Property The Zero Product Property states that if ab=0,ab=0,ab=0, then either a=0,b=0,a=0, b=0,a=0,b=0, or both aaa and bbb equal 0.0.0. This property will be very …
By Caroline K
Problems 25
- Using the Zero Product Property, find all solutions to: 0=(2x−3)(6+x)0=(2x-3)(6+x)0=(2x−3)(6+x)
- Using the Zero Product Property, find the root(s) of the function y(x)=(x−0.5)(3−6x).y(x) = (x-0.5)(3-6x).y(x)=(x−0.5)(3−6x). Select all that apply.
- Factor and use the zero product property to find the solution(s) to the equation: 0=x3−4x0=x^3-4x0=x3−4x
- Using the Zero Product Property, find all real solution(s) to: 0=(x3−1)(5x+25)0=(x^3-1)(5x+25)0=(x3−1)(5x+25)
- How many real roots does x3+x2=−x−1x^3+x^2 = -x-1x3+x2=−x−1 have?
- Jared wants to make a box. The possible heights xxx of the box satisfy the equation x3−4x2−x+4=0x^3-4x^2-x+4 = 0x3−4x2−x+4=0. Select the heights that the box can be.
- Concept check: If a⋅b=0a\cdot b=0a⋅b=0, which of the following must be true?
- What are some possible explanations?
- What is a possibility?
- Which of the following could be true?
- Lucy is practicing multiplication with her mom's grocery receipt. She is surprised when the total product of all the prices on the whole (nonempty) receipt is equal to zero! Whi…
- What is the minimum number of variables equal to zero such that this equation holds?
- Danny has 101101101 Dalmatians in 102102102 doghouses. If Danny were to multiply together the numbers of dogs in each doghouse, what would be their product?
- Given that (a−4)(b−3)(c−2)=0(a-4)(b-3)(c-2)=0(a−4)(b−3)(c−2)=0 and a,b,c≤2a,b,c \le 2a,b,c≤2, what can we conclude about ccc?
- Given that (a−1)(b−2)(c−3)=0(a-1)(b-2)(c-3)=0(a−1)(b−2)(c−3)=0 and a,b,c>2a,b,c > 2a,b,c>2 (a,b,a,b,a,b, and ccc are all greater than 222), what can we conclude about ccc?
- Use the zero product property to find the roots of: f(x)=(2x−8)(x+3)f(x)=(2x-8)(x+3)f(x)=(2x−8)(x+3)
- Use the zero product property to find the roots of: f(x)=(6x−18)(−9x+45)f(x)=(6x-18)(-9x+45)f(x)=(6x−18)(−9x+45)
- Solve for xxx. 6x3+9x2−15xx−1=0\frac{6x^3+9x^2-15x}{x-1}=0x−16x3+9x2−15x=0
- (x+a)(x+b)=0(x+a)(x+b) = 0(x+a)(x+b)=0 If aaa and bbb are defined constants, which expressions can you set to 000 to solve for possible values of xxx? Check all that apply.
- (x+a)(x+b)=0(x+a)(x+b) = 0(x+a)(x+b)=0 If aaa and bbb are constants, what could be the solutions to this equation? Check all that apply.
- (x−a)(x−b)=0(x-a)(x-b) = 0(x−a)(x−b)=0 If aaa and bbb are constants, what could be the solutions to this equation? Check all that apply.
- (x−a)(x−b)=0(x-a)(x-b) = 0(x−a)(x−b)=0 If aaa and bbb are defined constants, which expressions can you set to 000 to solve for possible values of xxx? Check all that apply.
- x2+kx+c=(x+a)(x+b)x2+kx+c=0\begin{array}{rcl} x^2 + kx + c &=& (x+a)(x+b) \\ x^2 + kx + c &=& 0 \end{array}x2+kx+cx2+kx+c==(x+a)(x+b)0 If kkk and ccc are defined constants, w…
- To solve the quadratic equation x2+bx=cx^2 + bx = cx2+bx=c for xxx using the zero product property, what should be the first step?
- Which of the following could be possible values of (j,k)(j,k)(j,k)? Check all that apply.