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If a,b,c ∈ R and ax^2 + bx + c =0 has no real roots, then a. c(a+b+c) >0 b. c-c(a+b+c) >0 c. c+ c(a-b-c) >0 d. c(a-b-c) >0

If a,b,c ∈ R and ax^2 + bx + c =0 has no real roots, then a. c(a+b+c) >0 b. c-c(a+b+c) >0 c. c+ c(a-b-c) >0 d. c(a-b-c) >0

Grade:12th pass

2 Answers

Arun
25750 Points
6 years ago
If a,b,c ∈ R and ax^2 + bx + c =0 has no real roots, then c * (a+ b+c) >0 Hence option A is correct.
 
 
Regards
Arun
Samyak Jain
333 Points
5 years ago
a,b,c ∈ R    and    ax^2 + bx + c =0 has no real roots. 
\therefore  discriminant or D > 0 
So for any x \in R,  f(x) = ax^2 + bx + c is always greater than zero.
Put x = 0 in f(x) 
f(0)  =  a*0 + b*0 + c = c  
f(1)  =  a + b + c 
\because    f(x)  >  0     \forall  x \in R
\therefore    f(0) > 0 ,  f(1) > 0   i.e.   c > 0 ,   (a + b + c) > 0
Hence, c*(a + b + c) > 0
Option A is correct.

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