Respuesta :

bluegreen24

Answer: [tex][-\frac{1}{4}, \frac{3}{2}][/tex]

Step-by-step explanation:

Factor:

  • [tex]g(x) = 8x^{2} -10x-3[/tex]
  • [tex]g(x) = x^{2} -10x-24[/tex] ---> multiply constant (3) by coefficient of first term
  • [tex]g(x) = (x+\frac{2}{8})(x-\frac{12}{8} )[/tex] ---> factor (multiplies to 24 and adds to -10. Divide factors by 8 since you multiplied by 8 in previous step)
  • [tex]g(x) = (x+\frac{1}{4})(x-\frac{3}{2})[/tex] ---> simplify
  • [tex]g(x) = (4x+1)(2x-3)[/tex] ---> move denominator of fraction to be coefficient of x

Solve:

  • [tex]0 = (4x+1)(2x-3)[/tex] ---> set equation equal to 0.
  • [tex]0 = 4x + 1[/tex] ---> make each parentheses equal to 0.
  • [tex]-1 = 4x[/tex]
  • [tex]-\frac{1}{4} = x[/tex] ---> x intercept
  • [tex]0 = 2x - 3[/tex]
  • [tex]3 = 2x[/tex]
  • [tex]\frac{3}{2} = x[/tex] ----> x intercept

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