If the following equation has no real roots, what are the possible values of p for #x^2 + (3p+1)x - p = 0#?
3 Answers
Explanation:
We know that, the quadr. eqn.,
Therefore, in our case, we must have,
Case (1) :
Similarly, in Case (2) , we have,
We conclude that,
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If it has no real roots, then the discriminant of quadratic formula
Analyze this last expresion: represents a parabola for all values of p. Lets determine his roots
So in our case, the values of p for which the first equation has not real roots are in the interval
Explanation:
If a quadratic equation has no real roots then its discriminant is less than zero. The discriminant of general quadratic equation
We have the equation
=
Hence if
Now there are two possibilities
(1)
(2)
Hence for
we must have