# 5 . ( a ) First design a polynomial that has 1 + V/ 5 – V 2 as a root , and then use RRI , the Rational Roots Theorem , to show this number must be

a.First design a polynomial that has 1 + 3√5 −√2 as a root, and then use RRT, the Rational Roots Theorem, to show this number must be irrational.

b.Let a be a rational number. Use RRT to determine whether the polynomial p(x) = x^3−a√5x−1has a rational root? (Hint: Design another polynomial with rational coefficients that shares the rootsof p(x).)5 . ( a ) First design a polynomial that has 1 + V/ 5 – V 2 as a root , and then use RRI , the RationalRoots Theorem , to show this number must be irrational .5 . ( b ) Let a be a rational number . Use RRI to determine whether the polynomial p ( a ) = 23 – av 5 * – 1has a rational root ? ( Hint : Design another polynomial with rational coefficients that shares the rootsof p ( ac ) . )

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