Past Papers’ Solutions  Edexcel  AS & A level  Mathematics  Core Mathematics 1 (C16663/01)  Year 2015  June  Q#5
Hits: 41
Question
The equation
, where p is a constant
has no real roots.
a. Show that p satisfies
p^{2 }– 6p +1 > 0
b. Hence, find the set of possible values of p.
Solution
a.
We are given that;
We are given that given equation has no real solutions of x (roots).
For a quadratic equation , the expression for solution is;
Where
If
If
If
Since given is a quadratic equation with no real solutions of x (roots), its discriminant must be;
b.
We are required to solve the inequality;
We solve the following equation to find critical values of
For a quadratic equation
Therefore;
Now we have two options;



Hence the critical points on the curve for the given condition are
Standard form of quadratic equation is;
The graph of quadratic equation is a parabola. If
If
We recognize that
Therefore conditions for
Comments