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If X – 2 is a Factor of X2 + Ax + B and a + B = 1, Find the Values of a and B. - ICSE Class 10 - Mathematics

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Question

if x – 2 is a factor of x2 + ax + b and a + b = 1, find the values of a and b.

Solution

Let f(x) = x2 + ax + b
Since, (x – 2) is a factor of f(x).
 ∴ Remainder = f(2) = 0
(2)2 + a(2) + b = 0
4 + 2a + b = 0
2a + b = -4 …(i)
It is given that:
a + b = 1 …(ii)
Subtracting (ii) from (i), we get,
a = -5
Substituting the value of a in (ii), we get,
b = 1 – (-5) = 6  

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Solution If X – 2 is a Factor of X2 + Ax + B and a + B = 1, Find the Values of a and B. Concept: Factor Theorem.
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