Verify that the numbers given alongside the cubic polynomials below are their zeroes: Also verify the relationship between the zeroes and the coefficients in each case: (ii) x2 – 3x2 + 3x - 1;(1, 1, 1)
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p(x)=2x3+x2−5x+2 .... (1)
Zeroes for this polynomial are 21,1,−2
Substitute the x=21 in equation (1)
p(21)=2(21)3+(21)2−5(21)+2
=41+41+25+2
=0
Substitute the x=1 in equation (1)
p(1)=2×13+12−5×1+2
=2+1−5+2=0
Substitute the x=−2 in equation (1)
p(−2)=2(−2)3+(−2)2−5(−2)+2
=−16+4+10+2=0
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