Question

if x=-1/3 is a zero polynomial p(x)= 27x^3 -ax^2 -x +3 then find the value of a

Answer 1

If X = -1/3
P(X)=27X^3 - aX^2 -X+3 = 0
P(1/3)=27(-1/3)^3 -a(-1/3)^2 -(-1/3) +3 =0
=>27(-1/27) -a(-1/9) +1/3 +3 = 0
=>-1+(a/9) +1/3 +3 =0
=>(-9+a+3+27)/9 =0
=>(-9+a+3+27)= 0
=> a+21 =0
=>a =(-21)

Answer 2

Given,

A polynomial p(x)= 27x^3 - ax^2 - x + 3

x=-1/3 is a zero of p(x)

To find,

The value of a.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

If n is a root of a polynomial p(x), then the value of p(x) at x = a is equal to zero.

Now, according to the question;

x=-1/3 is a zero of p(x)

=> p(-1/3) = 0

=> 27(-1/3)^3 - a(-1/3)^2 - (-1/3) + 3 = 0

=> -1 - a/9 + 1/3 + 3 = 0

=> (-9 - a + 3 + 27)/9 = 0

=> 21 - a = 0

=> a = 21

Hence, the value of a is equal to 21.