Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:
(i) 2x3 + x2 - 5x + 2; 1/2, 1, -2
(ii) x3 - 4x2 + 5x - 2; 2, 1, 1
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Answers
☆ Answer
f(x)=2x3+x2−5x+2
f(21)=2(31)3+(21)2−5(21)+2
=41+41−25+2=0
f(1)=2(1)3+(1)2−5(1)+2=2+1−5+2=0,
f(−2)=2(−2)3+(−2)52(−2)+2=−16+4+10+2=0.
Let α=21,β=1, and γ=−2
Now, Sum of zeros =α+β+γ=21+1
Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:
(i) 2x3 + x2 - 5x + 2; 1/2, 1, -2
(ii) x3 - 4x2 + 5x - 2; 2, 1, 1
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