A biquadratic

Algebra Level 2

The biquadratic equation x 4 − 5 x 2 + 6 = 0 x^4 - 5x^2 + 6=0 has 4 real roots.

Let L L be the largest of the roots and S S be the smallest of the roots.

Find L − S L - S .

Give your answer to 3 decimal places.


The answer is 3.464.

Denton Young by Denton Young , 47, USA

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1 solution

Denton Young
Dec 20, 2016

The equation is easily factored as ( x 2 − 2 ) ( x 2 − 3 ) (x^2 - 2)(x^2 - 3)

The roots of this equation are therefore 2 \sqrt{2} , − 2 -\sqrt{2} , 3 \sqrt{3} and − 3 -\sqrt{3}

So L − S L - S = 2 3 2\sqrt{3} = 3.464 3.464

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