Question

The polynomial  is denoted by .

    i.       Find the value of the constant  for which

   ii.       Hence solve the equation , giving your answers in an exact form.

Solution

    i.
 

We are given that;

We are also given that;

We equate the two equations.

We can expand the R.H.S.

Comparing terms on both sides of the equation;

Since we are looking for value of constant  and there are two equations containing constant ;

Hence;

  ii.
 

We are required to solve the equation;

We are given that;

Therefore;

We are also given that;

We have found in (i) that ; therefore;

Hence;

Now we have two options.

These are both quadratic equations and we need to solve them for .

Standard form of quadratic equation is;

Solution of a quadratic equation is expressed as;

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