i) If the roots of the quadratic equation  are  and . Find a quadratic equation whose roots are  and .
(ii) Given that , find the two values of p for which the equation  has real
roots.

Given that a is a real constant, prove that the roots  and  of the quadratic equation
 are real. Find the value of a in the case where .

Given that  and  are the roots of the equation , where b is a constant, find the quadratic equation whose roots are  and .

The roots of the equation  are  and . Form a quadratic equation with roots  and .

The equation  has roots  and . Find without solving this equation, the values of  for which
a)
b) .

(i) Find the range of values of  for which the equation  has
a) Real roots
b) Imaginary roots.
(ii) The roots of the equation  are  and . Without solving this equation form the quadratic equation whose roots are  and .

Show that if  and  are the roots of the quadratic equation , where  are real constants then . The roots of the quadratic equation , where b is a real constant are .  and . Find in terms of , the quadratic equation whose roots are  and  where , . Hence, find the range of values of b for which  and  are real and distinct.

Given that  and  are roots of an equation  where , show that

  Given that  are the roots of the equation . Find the quadratic equation whose
roots are
a)  and
b)  and .

Given that the roots of the equation  arc  and , form the equation whose roots are  and . Find the values of r for which  and  are equal.