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Question -

If x + 2 is a factor 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



Answer -

(b) x + 2 is a factor of x2 + ax + 2b and a +b = 4
x + 2 is one of the factor
x = – 2 is its one zero
f(-2) = 0
=> (-2)2 + a (-2) + 2b = 0
=> 4 – 2a + 2b = 0
=> 2a – 2b = 4
=> a – b = 2
But a + b = 4
Adding we get, 2a = 6 => a = 3
and a + b = 4 => 3 + b = 4 => b = 4 – 3 = 1
a = 3, b = 1

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