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# Use ZPP. Find all the solutions to each equation. a. $(x-2)(x+1) = 0$ b. $(2x-3)(x+5) = 0$ c. $3x(x+8) = 0$ d. $x^2-4x = 0$

Solution

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Solve the given equation as shown below, follow the steps:

a) $(x-2)(x+1)=0\qquad$ [zero product property]

$x-2=0\Rightarrow x=2$

$x+1=0\Rightarrow x=-1$

b) $(2x-3)(x+5)=0\qquad$ [zero product property]

$2x-3=0\Rightarrow 2x=3\Rightarrow x=\dfrac{3}{2}$

$x+5=0\Rightarrow x=-5$

c) $3x(x+8)=0\qquad$ [zero product property]

$3x=0\Rightarrow x=0$

$x+8=0\Rightarrow x=-8$

d) $x^2-4x=0\qquad$ [factor out $x$]

$\Rightarrow x(x-4)=0\qquad$ [zero product property]

$x=0$

$x-4=0\Rightarrow x=4$

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