Question

If x³+ax²+bx+6 has x-2 as a factor and leaves a remainder 3 when devided by x-3,find the values of a and b

Answer 1

Hey friend☺

Let p ( x ) = x^3 + ax^3 + bx + 6

x - 2 is a factor of p ( x )

Hence p ( 2 ) = 0

p ( 2 ) = x^3 + ax^2 + bx + 6

》0 = ( 2 )^3 + a ( 2 )^2 + b ( 2 ) + 6

》0 = 8 + 4a + 2b + 6

》0 = 14 + 4a + 2b

》4a + 2b = - 14

》2a + b = - 7. ... ( 1 )

if p ( x ) is divided by x - 3 remainder is 3

So p ( 3 ) = 3

p ( 3 ) = x^3 + ax^2 + bx + 6

》3 = ( 3 )^3 + a( 3 )^2 + 3b + 6

》3 = 27 + 9a + 3a + 6

》3 = 33 + 9a + 3a

》9a + 3b = - 30

》3a + b = - 10. ... ( 2 )

Subtracting equation ( 1 ) from ( 2 ) we get

a = - 3

Hope it helps you ..!!

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