find a for which `ax^(2) + x -1lt 0,AA x in R ?`

find a for which 3x^(2) + ax+3 gt 0,AA x in R.

The least value of alpha in R for which 4ax^2+(1)/(x)ge1 , for all xgt 0 , is

Let f(x) = x - x^(2) and g(x) = {x}, AA x in R where denotes fractional part function. Statement I f(g(x)) will be continuous, AA x in R . Statement II f(0) = f(1) and g(x) is periodic with period 1.

If the tangent to the curve y = 1 – x^(2) at x = alpha , where 0 lt alpha lt 1, meets the axes at P and Q. Also alpha varies, the minimum value of the area of the triangle OPQ is k times area bounded by the axes and the part of the curve for which 0 lt x lt 1 , then k is equal to

If alpha, beta be the roots of 4x^(2) - 16x + c = 0, c in R such that 1 lt alpha lt 2 and 2 lt beta lt 3 , then the number of integral values of c is

Sketch the graph for y=tan^(-1)x, AA x in R.

Let f(x) be a fourth differentiable function such f(2x^2-1)=2xf(x)AA x in R, then f^(iv)(0) is equal

Find all values of 'm' which (2m-3)x^(2)+2mx+4 lt 0 for all real x.

If a and b ( != 0) are roots of x^(2) +ax + b = 0 , then the least value of x^(2) +ax + b ( x in R) is :

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .