Question

If x=-1\3 is a zero of a polynomial p(x)=27xcube -axsquare -x+3 then find the value of a

Answer 1

a = 21

Explanation:

If x = h is a zero of a polynomial then f(h) = 0, thus

p(-
`(1)/(3)` ) = 27( -
`(1)/(3)` )³ - a(-
`(1)/(3)` ) - (-
`(1)/(3)` ) + 3 = 0, that is

27 (-
`(1)/(27)` ) -
`(1)/(9)` a +
`(1)/(3)` + 3 = 0

- 1 -
`(1)/(9)` a +
`(10)/(3)` = 0 ( multiply through by 9 to clear the fractions )

- 9 - a + 30 = 0

- a + 21 = 0 ( subtract 21 from both sides )

- a = - 21 ( multiply both sides by - 1 )

a = 21