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  4. If quadratic equation x2-3 a x+a2=9 has roots of opposite sign, then the sum of all possible values of a equals

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Q. If quadratic equation $x^2-3 a x+a^2=9$ has roots of opposite sign, then the sum of all possible values of a equals

Complex Numbers and Quadratic Equations

Solution:

$\because$ Roots of quadratic $x^2-3 a x+a^2=9$ are opposite sign
$\therefore a^2-9< 0 \Rightarrow-3< a< 3$
$\therefore$ Sum of all possible values of $a=0$.