Let R be the set of real numbers and the functions f : R ➔ R and g : R ➔ R be defined by f(x) = x2 + 2x - 3 and g(x) = x + 1. Then, the value of x for which f(g(x)) = g(f(x)) is
- 1
0
1
2
Let f(x) = ax2 + bx + c, g(x) = px2 + qx + r such that f(1) = g(1), f(2) = g(2) and f(3) - g(3) = 2. Then, f(4) - g(4) is
4
5
6
7
The equations x2 + x + a= 0 and x2 + ax + 1 = 0 have a common real root
for no value of a
for exactly one value of a
for exactly two value of a
for exactly three value of a
The points representing the complex number z for which arg lie on
a circle
a straight line
an ellipse
a parabola
The quadratic equation 2x2 - (a3 + 8a - 1)x + a2 - 4a = 0 posses roots of opposite sign. Then,
a 0
0 < a < 4
Determine the sum of imaginary roots of the equation (2x + x - 1) ( 4x2 + 2x - 3) = 6
Given, (2x + x - 1) ( 4x2 + 2x - 3) = 6
Put 2x2 + x = y
Discriminants,
D1 = 1 + 4 x 3 = 13 > 0, real roots
D2 = 4 - 16 = - 12 < 0, imaginary roots
Sum of roots of 4x + 2x + 1 = 0 is