a , b , c ∈ R , a ≠ 0 and the quadratic equation ax² + bx + c has no real roots,then (a) a + b + c > 0 , (b) a(a + b + c) > 0 , (c) b( a + b + c ) > 0 , (d) c(a + b + c) > 0

Asked by yeeshuraj3 | 10th Sep, 2016, 05:15: PM

Expert Answer:

begin mathsize 16px style space a x ² space plus space b x space plus space c space h a s space n o space r e a l space r o o t s space D less than 0 comma
a H left parenthesis x right parenthesis greater than 0 space comma space for all space x space element of straight real numbers space comma space W h e r e space H left parenthesis x right parenthesis space equals space a x ² space plus space b x space plus space c space
I n space G e n e r a l comma
a H left parenthesis 1 right parenthesis space greater than space 0 space S o comma space a left parenthesis a space plus b space plus space c space right parenthesis greater than 0
a H left parenthesis 0 right parenthesis space greater than space 0 space s o comma space a c greater than 0
f r o m space a b o v e space w e space c a n space s a y
c left parenthesis a plus b plus c right parenthesis greater than 0
W h i c h space i s space o p t i o n space d.

end style

Answered by Tripti Agrawal | 12th Sep, 2016, 05:03: PM