Question

Find the value of a and b so that polynomial xcube -axsaquare -13 +b has (x-1) and (x+3) as factor

Answer 1

Hey Friend ☺

Let the p ( x ) = x^3 - ax^2 - 13x + b

p ( x ) has two factors ( x - 1 ) & ( x + 3 )

So p ( 1 ) = 0 and p ( - 3 ) = 0

So

p ( 1 ) = x^3 - ax^2 - 13x + b

》0 = ( 1 )^3 - a ( 1 )^2 - 13 ( 1 ) + b

》0 = 1 - a - 13 + b

》0 = - 12 - a + b

》 a - b = - 12. ... ( l )

p ( - 3 ) = x^3 - ax^2 - 13x + b

》0 = ( - 3 )^3 - a ( - 3 )^2 - 13 ( - 3 ) + b

》0 = - 27 - 9a + 39 + b

》0 = 12 - 9a + b

》- 9a + b = - 12. ... ( 'll )

Adding equation ( l ) & ( 'll ) we get

- 8a = - 24

》a = - 24/- 8

》a = 3

Putting a = 3 in equation ( l ) we get

- 3 - b = - 12

》b = 12 - 3

》b = 9

Hope it helps you ..!!

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