Find the x-intercepts of the polynomial function k(x)=4x(1−2x)(3x+4)

Question

.(1 point)
Responses

(−43,0)
, (0,0)
, (2,0)
left parenthesis negative Start Fraction 4 over 3 End Fraction comma 0 right parenthesis , left parenthesis 0 comma 0 right parenthesis , left parenthesis 2 comma 0 right parenthesis

(−43,0)
, (0,0)
, (12,0)
left parenthesis negative Start Fraction 4 over 3 End Fraction comma 0 right parenthesis , left parenthesis 0 comma 0 right parenthesis , left parenthesis Start Fraction 1 over 2 End Fraction comma 0 right parenthesis

(−43,0)
, (12,0)
, (4,0)

left parenthesis negative Start Fraction 4 over 3 End Fraction comma 0 right parenthesis , left ​parenthesis Start Fraction 1 over 2 End Fraction comma 0 right parenthesis , left parenthesis 4 comma 0 right parenthesis

(−43,0)
, (2,0)
, (4,0)
respond in normal english not code

Answer 1

To find the x-intercepts of the polynomial function \( k(x) = 4x(1 - 2x)(3x + 4) \), we need to set \( k(x) = 0 \) and solve for \( x \).

The function \( k(x) \) will be zero when any of its factors are zero:

1. \( 4x = 0 \)

   • This gives \( x = 0 \).

2. \( 1 - 2x = 0 \)

   • Solving this gives \( 2x = 1 \) or \( x = \frac{1}{2} \).

3. \( 3x + 4 = 0 \)

   • Solving this gives \( 3x = -4 \) or \( x = -\frac{4}{3} \).

Thus, the x-intercepts of the polynomial function are:

• \( (0, 0) \)
• \( \left(\frac{1}{2}, 0\right) \)
• \( \left(-\frac{4}{3}, 0\right) \)

Therefore, the correct response for the x-intercepts is: \(\left(-\frac{4}{3}, 0\right), \left(0, 0\right), \left(\frac{1}{2}, 0\right)\).