Given that x minus root 5 is the factor of polynomial x ki power 3 minus 3 root 5 x square - 5 x + 15 root 5 find all the zeros of the polynomial
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x-√5 is a factor of x³-3√5 x²-5x+15√5
∴x³-3√5 x²-5 x +15√5 /x-√5
=x²-2√5 x-15
=x²-3√5 x +√5 x -15
=x(x-3√5)+√5(x-3√5)
=(x+√5)(x-3√5)
other zeroes are -√5 and 3√5
∴x³-3√5 x²-5 x +15√5 /x-√5
=x²-2√5 x-15
=x²-3√5 x +√5 x -15
=x(x-3√5)+√5(x-3√5)
=(x+√5)(x-3√5)
other zeroes are -√5 and 3√5
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