Prove that
My Self Assessment
Prove that with regard to the quadratic if the equation has one real root then
Prove that with regard to the quadratic if the equation has two equal roots, then
Find the roots of and show that the points which represent them are collinear.
Show that the roots of are the values of where r = 0, 1, 2 . . . ., n – 1, but omitting if n is even.
The conjugate of a complex number is . Then the complex number is
a)
b)
c)
d)
The quadratic equations and have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is
a) 2
b) 1
c) 4
d) 3
If then the maximum value of |z + 1| is
a) 4
b) 11
c) 6
d) 0
If the difference between the roots of the equation is less than then the set of possible values of a is
If the roots of the quadratic equation are tan30° and tan15° respectively then the value of 2 + q – p is
a) 3
b) 0
c) 1
d) 2
The value of is
a) 1
b) – 1
c) – i
d) i
The values of m for which both the roots of the equation are greater than – 2 and less than 4 lie in the interval
a) m > 3
b) – 1 < m < 3
c) 1 < m < 4
d) – 2 < m < 0
If where z is a complex number then the value of is
a) 54
b) 6
c) 12
d) 18
If the cube roots of unity are then the roots of the equation are
If z and are two non-zero complex numbers such that then is equal to
c) –π
The value of a for which the sum of the squares of the roots of the equation assumes the least value is
b) 3
c) 0
d) 1
If and then z lies on
a) A parabola
b) A straight line
c) A circle
d) An ellipse
If both the roots of the quadratic equation are less than 5 then k lies in the interval
a) [4, 5]
d) (5, 6]
Let z, w be complex numbers such that and then arg (z) equals
a) π/4
b) π/2
c) 3π/4
d) 5π/4
If and then is equal to
b) –1
c) 2
d) –2
If then z lies on
a) The real axis
b) The imaginary axis
If is a root of quadratic equation then its roots are
a) 0, 1
b) 1, 1
c) 0,
If one root of the equation is 4 while the equation has equal roots then the value of q is
a) 49/4
b) 12
c) 3
d) 4
