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in Polynomials by (36.4k points)
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If x + 2 is a factor of x2 + ax + 2b and a + b = 4, then

A. a = 1, b = 3

B. a = 3, b = 1

C. a = – 1, b = 5

D. a = 5, b = – 1

1 Answer

+1 vote
by (38.0k points)
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Best answer

Given;

A factor = x + 2

So,

x + 2 = 0

x = – 2

p(x) = x2 + ax + 2b

p( – 2) = ( – 2)2 + ( – 2)a + 2b

0 = 4 – 2a + 2b

– 4 = – 2 (a – b)

2 = a – b……………Equation (i)

4 = a + b …….. Equation (ii)

By Adding (i) and (ii) we get,

2 – a + b + 4 – a – b = – 2a + 2

2a = 2

So we get,

a = 3 and b = 1

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