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
Let a, b, c be three real numbers, such that a + 2b + 4c = 0, Then, the equation ax2 + bx + c = 0
has both the roots complex
has its roots lying within - 1 < x < 0
has one of roots equal to
has its roots lying within 2 < x < 6
If are the roots of the equation x2 + x + 1 = 0, then the equation whose roots are is
x2 - x - 1 = 0
x2 - x + 1 = 0
x2 + x - 1 = 0
x2 + x + 1 = 0
For the real parameter t, the locus of the complex number in the complex plane is
an ellipse
a parabola
a circle
a hyperbola
B.
a parabola
Let z = x + iy
On equating real and imaginary parts, we get
Hence, it represents a parabola.