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Question

a, b, c, are real numbers in the polynomial , p(z)=2z4+az3+bz2+cz+3. If two roots of the equation p(z)=0 are 2 and i. Then which of the following are false .

A
a=112
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B
b=5
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C
c = 112
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D
a=-11
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Solution

The correct option is D a=-11
If i is a root of p(z)=0 then i must also be a root of p(z)=0
Let the other root be k
Product of roots is 322(i)(i)k=32k=34
Sum of roots is 2+ii+k=a2a=112
b2=2(i)+2(i)+2(k)+i(i)+i(34)i(34)b=5
c2=2(i)(i)+2(i)(k)+2(i)(k)+i(i)(k)c=112


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