Question

find the values of a and b so that thhe polynomial x^3- ax^2-13x+b has x-1 and x-3 as factors

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Answer 1

polynomial , x³ -ax² -13x + b has two factors ( x -1) and (x +3)

it means , x = 1 and -3   are the roots (zeros ) of x³ -ax² -13x + b .

so,

put x = 1 in polynomial ,.

(1)³ -a(1)² -13(1) + b = 0

1 - a -13 + b = 0

-a + b = 12 ---------(1)

put x = -3

(-3)³ -a(-3)² -13(-3) + b = 0

-27 -9a +39 + b = 0

-9a + b = -12 --------(2)

subtract equation (1) and (2)

-a + b + 9a - b = 12 + 12

8a = 24

a = 3

put a = 3 in equation (1)

b = 15

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