Question

Find the value of a and b if x-1 and x-2 are factors of expression if x^3-ax+b
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Answer 1

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Answer 2

Answer :

The polynomial would be x³ - 7x + 6

Explanation :

Since, (x - 1) and (x - 2) are the factors of p(x) = x³ - ax + b. x = 1 and 2 would be the zeros of the above polynomial

Putting x = 1,we write :

(1)³ - a(1) + b = 0

→ a - b = 1 ----------(1)

Putting x = 2,we write :

(2)³ - 2a + b = 0

→ 2a - b = 8------------(2)

Subtracting equation (1) from (2),

(2a - b) - (a - b) = 8 - 1

→ a = 7

Putting a = 7 in equation (1),

7 - b = 1

→ b = 6

Hence,(a,b) = (7,6)