Question

When x cube minus 2 x square + a x minus b is divided by x cube minus 2 x minus 3 the remainder is x x minus 6 the value of a and b are respectively

Answer 1

$Let \: p(x) = x^{3}-2x^{2}+ax-b, \: \\g(x) = x^{3}-2x - 3 ,\:and \: the \: Remainder \: is \:(x-6)$

/* According to the problem given */

x³-2x-3) x³-2x²+ax-b (1

********** x³+ 0 -2x - 3

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Remainder= -2x²+(a+2)x+(3-b)

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$But \: Remainder = x-6 \: (given )$

$\implies -2x^{2}+(a+2)x+(3-b)= x - 6$

/* Compare bothsides,we get */

$i ) a + 2 = 1$

$\implies a = 1 - 2$

$\implies\pink { a = - 1 }$

$ii ) 3-b = -6$

$\implies - b = -6 - 3$

$\implies - b = - 9$

$\implies \blue {b = 9}$

Therefore.,

$\green { a = -1 \: and \: b = 9 }$

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