# 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) :**

**impossible.**

Similarly, in **Case (2)** , we have,

We conclude that,

**Enjoy Maths.!**

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