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Composite Function

FIND A FOURTH...

Question

FIND A FOURTH DEGREE EQUATION WITH RATIONAL COEFFICIENTS, ONE OF WHOSE ROOTS IS (√3 + √7)

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Q. The equation of fourth degree with rational coefficients one of whose roots is

\sqrt{3} + \sqrt{2}

Q. Form the equation of the fourth degree with rational coefficients, one of whose roots is

\sqrt{2} + \sqrt{- 3}

Q. Form the equation of the eighth degree with rational coefficients one of whose roots is

\sqrt{2} + \sqrt{3} + \sqrt{- 1}

Q. Form the quadratic equation with rational coefficients whose one of the root is:

\sqrt{3} - \sqrt{7}

Q. Assertion :If one root is

\sqrt{3} - \sqrt{2}

, then the equation of lowest degree with rational coefficients

x^{4} - 10 x^{2} + 1 = 0

Reason: For polynomial equation with rational coefficients irrational roots occurs in pairs.

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