Question

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

Answer 1

$Let \: p(x) = x^{2} + ax + b$

$If \: (x-2) \: is \:a \: factor \: of \: x^{2} + ax + b$

$then \: p(2) = 0$

$\implies 2^{2} + a\times 2 + b = 0$

$\implies 4 + 2a + b = 0 \: ---(1)$

$and \: a + b = 1 \: ---(2) \: (given)$

/* subtract equation (2) from equation (1) , we get*/

$\implies 4 + a = -1$

$\implies a = -1 - 4$

$\implies a = -5$

$Put \: a = -5 \: in \: equation \:(2), we \:get$

$\implies -5 + b = 1$

$\implies b = 1 + 5$

$\implies b = 6$

Therefore.,

$\green { a = -5 , \: and \: b = 6 }$

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