Let us define two functions
f (x) = ax2 + bx + c; a, b, c ∈ R & a ≠0
g (x) = dx2 + ex + f; d, e, f ∈ R & d ≠0
If both the equations has imaginary roots and real part of complex roots of both equation f(x) = 0 and
g(x) = 0 are same. If minimum value of f(x) is same as negative of maximum value of g(x) then
1. Which statement is correct?
(a) bd = e2
(b) bd = ea
(c) bc = ef
(d) none of these
8. If y = f (|x|), then
(a) Minimum value of y is same as minimum value of f(x)
(b) Minimum value of y is greater than minimum value of f(x)
(c) Minimum value of y is smaller than minimum value of f(x)
(d) (a) and (b) is correct
9. If y = |g (|x|)|, then
a) Minimum value of y is same as minimum value of f(x)
b) Minimum value of y is greater than minimum value of f(x)
c) Minimum value of y is smaller than minimum value of f(x)
d) (a) and (b) is correct
211)
f (x) = ax2 + bx + c; a, b, c ∈ R & a ≠0
g (x) = dx2 + ex + f; d, e, f ∈ R & d ≠0
given real part of both eqn is equal
root of f(x)=0 is -b±√b2-4ac2a
root of g(x)=0 is -e±√e2-4df2d
since real part is equal
-b2a = -e2d
bd=ae
hence option (b) correct