Question

If f(x)= 2x^3-12x^2+20x-16 and f(4)= 0, then find all the zeros of f(x) algebraically

Answer 1

Answer:

• x = 4 is the only real zero

Step-by-step explanation:

Find the zero's of f(x)

• 2x³ - 12x² + 20x - 16 = 0
• x³ - 6x² + 10x  - 8 = 0
• x³ - 4x² - 2x² + 8x + 2x - 8 = 0
• x²(x - 4) - 2x(x - 4) + 2(x - 4) = 0
• (x - 4)(x² - 2x + 2) = 0
• (x - 4)(x² - 2x + 1 + 1) = 0
• (x - 4)[(x - 1)² + 1] = 0

• x - 4 = 0 ⇒ x = 4, we already know this
• (x - 1)² + 1 = 0 ⇒ (x - 1)² = - 1, no real solution as the square is never negative