Question

Find the x-intercepts of the function g(x)=8x^{2} −10x−3

Answer 1

Answer:
`[-(1)/(4), (3)/(2)]`

Explanation:

Factor:

• 
  `g(x) = 8x^(2) -10x-3`

• 
  `g(x) = x^(2) -10x-24` ---> multiply constant (3) by coefficient of first term

• 
  `g(x) = (x+(2)/(8))(x-(12)/(8) )` ---> factor (multiplies to 24 and adds to -10. Divide factors by 8 since you multiplied by 8 in previous step)

• 
  `g(x) = (x+(1)/(4))(x-(3)/(2))` ---> simplify

• 
  `g(x) = (4x+1)(2x-3)` ---> move denominator of fraction to be coefficient of x

Solve:

• 
  `0 = (4x+1)(2x-3)` ---> set equation equal to 0.
• 
  `0 = 4x + 1` ---> make each parentheses equal to 0.
• 
  `-1 = 4x`
• 
  `-(1)/(4) = x` ---> x intercept
• 
  `0 = 2x - 3`
• 
  `3 = 2x`
• 
  `(3)/(2) = x` ----> x intercept