The expression y=ax2+bx+c has always the same sign as, c if

Let f(x)=ax2+bx+c. Then , f(0)=cThus, the curve y=f(x) meets y-axis at (0,c)If c > 0, then by hypothesis f( x)>0. This means that the curve y=f(x) does not meet x-axis. If c<0, then by hypothesis, f(x)<0, which means that the curve y=f(x) is always below x-axis and so it does not intersect with x-axis. Thus, in both the cases y=f(x) does not intersect with x-axis i.e. f(x)≠ 0 for any real x.Hence, f(x)=0i.e. ax2+bx+c=0 has imaginary roots and so we have b2<4ac