Question

1. (2x + 3)(x - 5) = 0 solutions: ____ roots: ____
2. (5x - 2)(x + 3) = 0 solutions: ____ roots: ____
3. x(2x - 3) = 0 solutions: ____ roots: ____

Explanation:

Problem 2: $(2x+3)(x-5)=0$

Step1: Set first factor to 0

$2x + 3 = 0$

Step2: Solve for $x$

$x = -\frac{3}{2}$

Step3: Set second factor to 0

$x - 5 = 0$

Step4: Solve for $x$

$x = 5$

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Problem 3: $(5x-2)(x+3)=0$

Step1: Set first factor to 0

$5x - 2 = 0$

Step2: Solve for $x$

$x = \frac{2}{5}$

Step3: Set second factor to 0

$x + 3 = 0$

Step4: Solve for $x$

$x = -3$

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Problem 4: $x(2x-3)=0$

Step1: Set first factor to 0

$x = 0$

Step2: Set second factor to 0

$2x - 3 = 0$

Step3: Solve for $x$

$x = \frac{3}{2}$

Answer:

Problem 2:

solutions: $x=-\frac{3}{2}, x=5$
roots: $-\frac{3}{2}, 5$

Problem 3:

solutions: $x=\frac{2}{5}, x=-3$
roots: $\frac{2}{5}, -3$

Problem 4:

solutions: $x=0, x=\frac{3}{2}$
roots: $0, \frac{3}{2}$