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  4. If a , b , c are real distinct numbers satisfying the condition a + b + c =0 then the roots of the quadratic equation 3 a x2+5 b x+7 c=0 are -

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Q. If $a , b , c$ are real distinct numbers satisfying the condition $a + b + c =0$ then the roots of the quadratic equation $3 a x^2+5 b x+7 c=0$ are -

Complex Numbers and Quadratic Equations

Solution:

$D=25 b^2-84 a c=25(a+c)^2-84 a c$
$(\because a+b+c=0)$
$=4(a+c)^2+21(a-c)^2>0$