If two roots of biquadratic equation x 4-12 x -5-0 are -1-2 and 1-2 i- Find the sum of the square of all the roots-

Since irrational roots and imaginary roots occurs in pairs. So, other roots are 1 √(2) and 1 √(2)i Sum of the square ( 1 + √(2))^2 + ( 1 √(2))^2 + (1+ ...

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Standard XII

Mathematics

Roots of a Quadratic Equation

If two roots ...

Question

If two roots of biquadratic equation $x^{4} + 12 x - 5 = 0$ are -1 + $\sqrt{2} a n d 1 + \sqrt{2} i$ . Find the sum of the square of all the roots.

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Solution

Since irrational roots and imaginary roots occurs in pairs.

So, other roots are $- 1 - \sqrt{2} a n d 1 - \sqrt{2} i$

Sum of the square

${(- 1 + \sqrt{2})}^{2} + {(- 1 - \sqrt{2})}^{2} + {(1 + \sqrt{2} i)}^{2} + {(1 - \sqrt{2} i)}^{2}$

$1 + 2 - 2 \sqrt{2} + 1 + 2 + 2 \sqrt{2}) + 1 - 2 + 2 \sqrt{2} i + 1 - 2 - 2 \sqrt{2} i$
6+2-4

=4.

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If two roots of biquadratic equation x4+12x−5=0 are -1 + √2 and 1+√2i . Find the sum of the square of all the roots. __

Since irrational roots and imaginary roots occurs in pairs. So, other roots are −1−√2 and 1−√2i Sum of the square (−1+√2)2+(−1−√2)2+(1+√2i)2+(1−√2i)2 1+2−2√2+1+2+2√2)+1−2+2√2i+1−2−2√2i 6+2-4 =4.

If two roots of biquadratic equation $x^{4} + 12 x - 5 = 0$ are -1 + $\sqrt{2} a n d 1 + \sqrt{2} i$ . Find the sum of the square of all the roots.

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