If `x^2+2ax+10-3a gt0` for all `x in R` then

If x^2-ax+1-2a^2 > 0 for all x in R, then ....

If x^(2)+2 a x+(10-3 a) gt 0 for all x, then

If x^(2)-ax+1-2a^(2)>0 for all x in R, then

If f'(x^2-4x+3)gt0 " for all " x in (2,3) then f(sinx) is increasing on

If f'(x^2-4x+3)gt0 " for all " x in (2,3) then f(sinx) is increasing on

Let f'(x)gt0 and g'(x)lt0 for all x in R, then

If f(x)gt0 and f"(x)gt0 forallx in R, then for any two real numbers x_1 and x_2,(x_1nex_2)

Let a, b, c in R with a gt 0 such that the equation ax^(2) + bcx + b^(3) + c^(3) - 4abc = 0 has non-real roots. If P(x) = ax^(2) + bx + c and Q(x) = ax^(2) + cx + b , then (a) P(x) gt 0 for all x in R and Q(x) lt 0 for all x in R . (b) P(x) lt 0 for all x in R and Q(x) gt 0 for all x in R . (c) neither P(x) gt 0 for all x in R nor Q(x) gt 0 for all x in R . (d) exactly one of P(x) or Q(x) is positive for all real x.