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 -

Question

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 - (A) positive (B) negative (C) real and distinct (D) imaginary

Tardigrade Admin · Accepted Answer

D=25 b2-84 a c=25(a+c)2-84 a c (∵ a+b+c=0) =4(a+c)2+21(a-c)2>0

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 -

positive

negative

real and distinct

imaginary

$D = 25 b^{2} - 84 a c = 25 (a + c)^{2} - 84 a c$
$(∵ a + b + c = 0)$
$= 4 (a + c)^{2} + 21 (a - c)^{2} > 0$

Q. If a,b,c are real distinct numbers satisfying the condition a+b+c=0 then the roots of the quadratic equation 3ax2+5bx+7c=0 are -