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

Answer:

a = 21

Step-by-step explanation:

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

p(- $\frac{1}{3}$ ) = 27( - $\frac{1}{3}$ )³ - a(- $\frac{1}{3}$ ) - (- $\frac{1}{3}$ ) + 3 = 0, that is

27 (- $\frac{1}{27}$ ) - $\frac{1}{9}$ a + $\frac{1}{3}$ + 3 = 0

- 1 - $\frac{1}{9}$ a + $\frac{10}{3}$ = 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