Q1. Complete the table of values for the given Quadratic Function and plot the curve against appropriate axis values:


(a)





(b) Using the Quadratic Formula, for each equation in the table above, evaluate the values of 'x' that satisfy the equations, ie: work out the roots of each quadratic.




Numerically the roots approximate to 3.414 and 0.586 to 3 d.p.





ATTENTION - We can go no further in this third case (not yet anyway) as the expression inside the "square root" is NEGATIVE, and would mean attempting to evaluate the square root of -15. The expression here is called "The Determinant" and has three potential outcomes:


  1. If the determinant is POSITIVE the quadratic expression / equation will have TWO REAL roots.
  2. If the determinant is ZERO the quadratic expression / equation will have TWO REAL roots of the SAME value (ie: ONE root)
  3. If the determinant is NEGATIVE the quadratic expression / equation will have NO REAL roots, it will have COMPLEX roots.


In the above case, the roots would be:


Where:





Complex numbers will come up in another section of this book, where the meaning of the entity 'i' will be explained.


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