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$|\begin{matrix} x^{4} & x^{2} & a \\ 3 & 1 & b \\ 0 & 0 & c \end{matrix}| = 0$ হলে, ‍a এর মান নির্ণয় কর।

0, \pm \sqrt{a}

0, \pm \sqrt{2}

0, \pm \sqrt{b}

0, \pm \sqrt{3}

0, \pm 3

ANSWER : 0

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<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mtable><mtr><mtd><msup><mi>x</mi><mn>4</mn></msup></mtd><mtd><msup><mi>x</mi><mn>2</mn></msup></mtd><mtd><mi>a</mi></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>1</mn></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mi>c</mi></mtd></mtr></mtable></mfenced><mo>=</mo><mn>0</mn></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x21d2;</mo><mi>c</mi><mfenced open="|" close="|"><mtable><mtr><mtd><msup><mi>x</mi><mn>4</mn></msup></mtd><mtd><msup><mi>x</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>=</mo><mn>0</mn></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x21d2;</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>0</mn><mo>&#xA0;</mo><mo>[</mo><mo>&#x2235;</mo><mi>c</mi><mo>&#x2260;</mo><mn>0</mn><mo>]</mo></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x21d2;</mo><msup><mi>x</mi><mn>2</mn></msup><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>)</mo><mo>=</mo><mn>0</mn></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x21d2;</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>0</mn><mo>,</mo><mo>&#xA0;</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>3</mn><mo>=</mo><mn>0</mn></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x21d2;</mo><mi>x</mi><mo>=</mo><mn>0</mn><mo>,</mo><mo>&#xb1;</mo><msqrt><mn>3</mn></msqrt></math>
N.B: মূল প্রশ্নে "a এর মান নির্ণয় কর"  এর পবিবর্তে "x এর মান নির্ণয় কর” হবে।

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