Question

find all the zeroes of x^3 - x^2 - 4x + 4 if one of its zero is -2​

Answer 1

Answer:

1 and 2

Step-by-step explanation:

x³-x²-4x+4=0

it can be written as

(x+2)(x²-3x+2)=0

x=-2,x²-x-2x+2=0

x(x-1)-2(x-1)=0

(x-1)(x-2)=0

x=1,x=2

Answer 2

Answer:

The zeros are –2, 2 and 1.

Step-by-step explanation:

Polynomial = x³ – x² – 4x + 4

Zero of the polynomial is –2

If –2 is the zero of polynomial, (x + 2) will be a factor of the given polynomial.

Divide the polynomial by (x + 2).

$\sf{ {x}^{2} - 3x + 2 }\\ \begin{array}{cc} \sf{x + 2} \overline{ \Big) \: \: \: \: \: \: \sf{x}^{3} - {x}^{2} - 4x + 4} \\ - \: \sf{ {x}^{3} + {2x}^{2} } \\ \!\!\!\!\!\! \!\!\!\!\! \: \: \: \: \: \: \: \: \: \: \: \:\blue - \: \: \: \: \: \: \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! \: \: \: \: \: \: \: \: \: \:\blue - \: \: \: \: \: \: \: \: \\ \overline{ \: \: \: \: \: \: \: \: \: \: \begin{gathered} \: \: \: \end{gathered} \: \: \: \: \: \: \sf{ { - 3x}^{2} - 4x }} \\ \: \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \sf{ { - 3x}^{2} - 6x} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \!\!\! \quad \!\!\!\!\!\!\!\!\!\!\!\! \: \: \: \: \: \: \:\blue + \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \!\!\!\!\!\!\!\!\!\!\!\! \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! \: \: \: \blue+ \\ \overline{ \begin{gathered} \\ \end{gathered} \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2x + 4 }} \\\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \: \: \:2x + 4} \\ \overline{ \sf{ \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:0 \: \: \: \: }} \end{array}$

Quotient = x² – 3x + 2

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Factorize x² – 3x + 2

$\rightarrow$ x² – 3x + 2

$\rightarrow$ x² – 2x – x + 2

$\rightarrow$ x(x – 1) – 2(x – 1)

$\rightarrow$ (x – 1)(x – 2)

Other factors of the polynomial are (x – 1) and (x – 2)

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★ Other zeros :

$\rightarrow$ (x – 1) = 0

$\rightarrow$ x = 1

$\rightarrow$ (x – 2) = 0

$\rightarrow$ x = 2

Therefore, the zeros are –2, 2 and 1.