Suppose f x is such a quadrant expression that it is positive for all real x If g x f x f rsquo x f ...........

Mathematics (NDA) Quadratic Equations

Suppose f(x) is such a quadrant expression that it is positive for all real x.

If g(x) = f(x) + f’(x) + f’’(x), then for any real x. Then for any real x.

g(x) < 0

g(x) > 0

g(x) = 0

g(x) $\geq$ 0

Let

f(x)=ax²+bx+c,a>0,b²<4ac

( $\because$ f(x)>0)
Now,

g(x)=ax²+bx+c+2ax+b+2a

=ax²+(b+2a)x+2a+b+c
Now,(b+2a)²−4a(2a+b+c)

=b²+4ab+4a²−8a²−4ab−4ac

=b²−4ac−8a²<0

⇒g(x)>0

Submit Error