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Question
If Z2+kZ+1−2i=0 has roots as z1 and z2, where z1=−i and k∈R, then the value of k is
If Z2+kZ+1−2i=0 has roots as z1 and z2, where z1=−i and k∈R, then the value of k is
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Solution
The correct option is A −2
Given equation is Z2+kZ+1−2i=0
Product of roots is
z1z2=1−2i⇒z2=1−2i−i⇒z2=2+i (∵1i=−i)
Sum of roots is
z1+z2=−k⇒k=−2
Alternate solution:
Given equation is Z2+kZ+1−2i=0 has roots as z1=−i, so putting it in the equation, we get
(−i)2+k(−i)+1−2i=0⇒−1−ki+1−2i=0∴k=−2
Given equation is Z2+kZ+1−2i=0
Product of roots is
z1z2=1−2i⇒z2=1−2i−i⇒z2=2+i (∵1i=−i)
Sum of roots is
z1+z2=−k⇒k=−2
Alternate solution:
Given equation is Z2+kZ+1−2i=0 has roots as z1=−i, so putting it in the equation, we get
(−i)2+k(−i)+1−2i=0⇒−1−ki+1−2i=0∴k=−2
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