Question

Find all the other zeroes of the polynomial x^4 - 2x^3 - 21x^2 + 62x - 40 if two of its zeroes are are 4 and -5

Answer 1

If two zeroes of polynomial is 4 and -5,

then (x -4 )(x+5)=0

x^2 + x -20 is one of the factor

by long division method,

quotient = x ^2 - 3 x +2

by splitting method,

x^2-2x -x -2

x ( x -2) - 1(x -2)

therefore x= 1 and 2

these are zeroes of polynomial

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