Which of the following statement is correct regarding Cu-extraction?&nbsp;

If&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math>&nbsp;is a root of the equation , &nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>&nbsp;</mo><mo>+</mo><mo> </mo><mi>k</mi><mi>x</mi><mo>&nbsp;</mo><mo>-</mo><mo>&nbsp;</mo><mfrac><mn>5</mn><mn>4</mn></mfrac><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn></math>, then the value of &nbsp;k is

If&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo>=</mo><msqrt><mn>7</mn></msqrt><mo>+</mo><msqrt><mn>3</mn></msqrt></math>&nbsp;and&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xy</mi><mo>=</mo><mn>4</mn></math>, then&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">x</mi><mn>4</mn></msup><mo>+</mo><msup><mi mathvariant="normal">y</mi><mn>4</mn></msup><mo>=</mo></math>

The polynomial equation&nbsp;<math class="SCXW136215543 BCX2" xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="SCXW136215543 BCX2"><mi>x</mi><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>+</mo><mn>8</mn><mo>=</mo><mo>(</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>)</mo><mo>(</mo><mi>x</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow></math>&nbsp;is&nbsp;

If&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>20</mn><mrow><mn>3</mn><mo>-</mo><mn>2</mn><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup></mrow></msup><mo>=</mo><msup><mfenced><mrow><mn>40</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mrow><mn>3</mn><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn></mrow></msup><mo>,</mo></math>&nbsp;then&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo>=</mo></math>

Which of the following statement is correct regarding Cu-extraction?

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