Question

Factor each quadratic and use the zero product property to find the solution
2x² - 5x = 3


X² + 6x + 5= 0

Answer 1

For the first quadratic, we will rearrange the equation as follows:
2x² - 5x - 3 = 0

Now, we will factor the quadratic:
(2x + 1)(x - 3) = 0

Now, we will use the zero product property to find the solutions:
2x + 1 = 0 or x - 3 = 0
2x = -1 or x = 3
x = -1/2 or x = 3

Therefore, the solutions to the equation 2x² - 5x = 3 are x = -1/2 and x = 3.

For the second quadratic, we will rearrange the equation as follows:
x² + 6x + 5 = 0

Now, we will factor the quadratic:
(x + 5)(x + 1) = 0

Now, we will use the zero product property to find the solutions:
x + 5 = 0 or x + 1 = 0
x = -5 or x = -1

Therefore, the solutions to the equation x² + 6x + 5 = 0 are x = -5 and x = -1.