Question

Please do step by steps for each!

#1) Find the polynomial with roots at 2 and 6

#2) Find the polynomial with a double root at -3 and another root at 4

#3) Find the polynomial with roots 0, -3 and 5

Answer 1

Answer:

• x² - 8x + 12
• x³ + 2x² - 15x - 36
• x³ -2x² - 15x

Step-by-step explanation:

#1) Find the polynomial with roots at 2 and 6

• (x -2)(x - 6) = x² - 8x + 12

#2) Find the polynomial with a double root at -3 and another root at 4

• (x+3)(x+3)(x-4) = (x²+6x+9)(x-4) = x³ + 2x² - 15x - 36

#3) Find the polynomial with roots 0, -3 and 5

• (x -0)(x+3)(x-5) = x(x²-2x - 15) = x³ -2x² - 15x