Question

Solve the equation 3x^3 - 28x^2 + 69x - 20 = 0 given that 4 is a zero of f(x) = 3x^3 - 28x^2 + 69x - 20.

a) 2
b) 3
c) 4
d) 5

Answer 1

To solve the equation 3x^3 - 28x^2 + 69x - 20 = 0 given that 4 is a zero of f(x) = 3x^3 - 28x^2 + 69x - 20, one can use the fact that if 4 is a zero, then (x - 4) is a factor of the equation. After factoring the equation, set each factor equal to zero and solve for x to find the solutions.

Step-by-step explanation:

To solve the equation 3x^3 - 28x^2 + 69x - 20 = 0 given that 4 is a zero of f(x) = 3x^3 - 28x^2 + 69x - 20, we can use the fact that if 4 is a zero, then (x - 4) is a factor of the equation. We can then perform long division or synthetic division to find the other factor. After factoring the equation, we can set each factor equal to zero and solve for x to find the solutions.

• To find the other factor, we can perform long division or synthetic division: (3x^3 - 28x^2 + 69x - 20) ÷ (x - 4) = 3x^2 - 16x + 5
• Setting each factor equal to zero: x - 4 = 0 and 3x^2 - 16x + 5 = 0
• Solving the equations: x = 4, x ≈ 0.33, x ≈ 1.52