Question

If (x + 1) and (x + 2) are the factors of the
polynomial xº + 13x2 + ax + b, find the
values of a and b.
​

Answer 1

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Let p(x) = x³+13x²+ax+b

Since (x+1) and (x+2) are factors of p(x),

-1 and -2 are the zeroes of the equation

Hence,

p(-1) = 0

p(-2) = 0

p(-1) = (-1)³ + 13(-1)² - a + b = 0

-1+13-a+b = 0

a-b = 12   ------(1)

p(-2) = (-2)³ + 13(-2)² -2a + b =0

b-2a = 8-52

b-2a = -48   -------(2)

(1)+(2) => a-b+b-2a = 12-48

-a = -36

a = 36

a-b = 12

b = a-12

b = 36-12

b = 24

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