Question

if alpha beta are zero of polynomial 3x^2+6x+k such that a^2+b^2+ab=8/3 then k=
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Answer 1

Answer:

since à and ß are the zeroes of given polynomial

3x²+6x+k

so, à+ß=-b/a=-6/3=-2

à.ß=à.ß=c/a=k/3

(à+ß)²=à²+ß²+2à.ß

(-2)²=a²+ß²+à.ß+à.ß

4=8/3+k/3. {à²+ß²+à.ß=8/3, given}

8+k=12

k=12/8

k=4/3