Question

Explain the zero product property. Give an example Showing how it is used to solve quadratic equations

Answer 1

when something is multiplied by 0, the result will be zero, so we can set other values and find an answer

(x+4)(x-5)=0 ; we can find values of x, by setting x+4 or x-5 to 0

so x+4=0 (x=-4)
so x-5 =0 (x=5)

so x is equal to both -4 and 5 for this equation

Answer 2

Zero product property:\[ab=0\iff a=0~or~b=0\]Suppose we are working on a quadratic equation like this one.\[x^2-5x-6=0\]which factors\[(x+1)(x-6)=0\]then by the zero product property, x+1=0 or x-6=0. This gives solutions of x=-1 or x=6.