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Quantitative Aptitude

HCF and LCM

If f x = x 2+...

Question

If $f (x) = x^{2} + 6 x + a, g (x) = x^{2} + 4 x + b, h (x) = x^{2} + 14 x + c$ and the LCM of f(x), g(x) and h(x) is (x + 8)(x - 2)(x - 6), then the value of a + b +c is

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Solution

$f (x) = x^{2} + 6 x + a$
$g (x) = x^{2} + 4 x + b$
$h (x) = x^{2} + 14 x + b$
LCM of f(x), g(x), h(x) = (x + 8)(x - 2)(x - 6)
If we take
$x + 8) (x - 2) = x^{2} + 6 x - 16 (x - 2) (x + 6) = x^{2} + 4 x - 12 (x + 6) (x + 8) = x^{2} + 14 x + 48$
So comparing we get a = -16, b = -12 and c = 48
$∴$ a+b+c = 20.

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