when are roots equal and real unequal and real imaginary

Check if the statement is true or false. "A quadratic equation with real coefficients cannot have exactly one imaginary root." => False or True..

All the q-th roots of z lie on a circle centred at the origin O and having radius equal to the real, positive q t h root of r. One of them has amplitude q /q and others are uniformly spaced around the circle separated from others by an angle 2p ..

Two complex numbers are equal iff their corresponding real parts and imaginary parts are separately equal..

Determine the nature of roots of the equation ( a 2 + b 2 ) x 2 - 2 b ( a+c ) x + ( b 2 + c 2 ) = 0 if a , b , c are in GP. => Negative and distinct or Positive and distinct or Imaginary or Real and equal..

The contributing structures do not have real existence. These are only imaginary structures, proposed to explain the properties of the molecule. None of these 'resonance structures' can be prepared in the laboratory. Only the resonance hybrid is the real molecule str..

Square root of a negative number is known as an imaginary number . If x and y are real numbers, then x + iy is called a complex number . x is called the real part and y is called the imaginary part . The following are the type..

. For the quadratic equations, we have i) b 2 - 4ac > 0 Roots are real and distinctii) b 2 - 4ac = 0 Roots are real and equaliii) b 2 - 4ac < 0 Roots are imaginary and distinct If the roots of ax2 + bx + c = 0, a( 0),b, c R..

The given equation can be split into n equations viz Each of these n equations represents straight lines through the origin. Hence the given equation represents n lines through the origin. It is to be noted that all the n straight lines need not be real and distinct. Some of them may be c..

Geometrical representation of a Complex number, Argand diagram - Since every complex number z = x + iy is an order pair of real numbers (x, y), it can therefore be represented by a point P(x,y) in the xy plane by taking the real part along the x-axis and the imaginary ..

Summary - If x and y are any real numbers, then x+iy is called a complex number. In the complex number x+iy, the real numbers x and y are respectively called the real part and imaginary part of x+iy. Two complex numbers are said to be equal if their..