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

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

The value of 'a' for which the equation x^(3) + ax + 1 = 0 and x^(4) + ax^(2) + 1 =0 has a common root is :

Let f : R to R be a function defined by f(x) = 4x - 3 AA x in R . Then Write f^(-1) .

Prove that the function f : R to R defined by f(x) = 3 - 4x , AA x in R is bijective.

If f : R to R is defined by f (x) =x ^(2) - 3x + 2, find f (f (x)).

f : R to R be defined as f(x) = 4x + 5 AA x in R show that f is invertible and find f^(-1) .

If the equations : x^(2) + 2x + 3 = 0 and ax^(2) + bx + c =0 a, b,c in R, Have a common root, then a: b : c is :

Find the values of 'a' for which -3<(x^2+ax-2)/(x^2+x+1)<2 is valid for all real x.

For the equation 3 x^(2)+p x+3=0, p gt 0 , if one root is square of the other, then p=

(x -2) is a factor of 2x^(3) + ax^(2) + bx - 14 and when divided by x-3, the remainder is 52 . Find the values of a and b .