Question

Find the zeros for 0 = 8x2 + 2x - 1 :

x = -1 and x = 8
x = 12 and x = -14
x = -12 and x = 14
x = -2 and x = 4
*must show work to receive credit*

Answer 1

x = -1/2 and x = 1/4

Explanation:

The equation ...

0 = 8x^2 +2x -1

can be factored* as ...

0 = (4x -1)(2x +1)

The solutions are the values of x that make these factors be zero:

4x -1 = 0 ⇒ x = 1/4

2x +1 = 0 ⇒ x = -1/2

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* The binomial factors will have coefficients of x that have a sum of 2 (the x-coefficient) and a product of 8·(-1) = -8. 4 and -2 satisfy this requirement. This knowledge lets us rewrite the equation and factor by grouping.

8x^2 +4x -2x -1 = 0 = 4x(2x +1) -1(2x +1) = (4x -1)(2x +1)