Question

If 1 is a zero of x3 – 3x2 – x + 3 then find all other zeroes

Answer 1

Answer:

x³-3x²-x+3=0

x²(x-3)-1(x-3)=0

x-3(x²-1)=0

(x-3)(x+1)(x-1)=0

Zeros of the polynomial are 3,1,-1.

Answer 2

The other two zeroes of the polynomial are 3 and -1.  

Step-by-step explanation:

we are given the following in the question:

$f(x) =x^3 - 3x^2 - x + 3$

1 is a root of given polynomial.

Thus, the given polynomial is divisible by (x-1).

Dividing the polynomial, we get,

$p(x) = \dfrac{x^3-3x^2-x+3}{x-1} = x^2-2x-3$

To obtain the zeroes of polynomial.

$p(x) = 0\\x^2-2x-3 = 0\\(x-3)(x+1)=0\\x = 3. x = -1$

Thus, the other two zeroes of the polynomial are 3 and -1.

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