Question

write the polynomial in x whose zeroes are 1,2 and-1​

Answer 1

f(x) = x³ - 2x²  - x + 2  whose zeroes are 1 , 2 & - 1

Step-by-step explanation:

polynomial in x whose zeroes are 1,2 and-1​

f(x)  = (x - 1)(x - 2)(x -(-1))

=> f(x) = (x - 1)(x - 2)(x + 1)

=> f(x) = (x - 2)(x² - 1)

=> f(x) =  x³ - x - 2x² + 2

=> f(x) = x³ - 2x²  - x + 2

Verification :

f(1) = 1³ - 2*1²  - 1 + 2  = 0

f(2) = 2³ - 2*2²  - 2+ 2  = 0

f(-1) = (-1)³ - 2*(-1)²  - (-1) + 2  = 0

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