Question

find the nature of the roots of the equation x^4+4x^3-20x^2+10=0​

Answer 1

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Given:  

To find: The nature of its roots.

Answer:

In order to find the nature of the roots of an equation, we solve its discriminant (D).

If    were an equation, its discriminant would be given by:

                                                   

From the given equation (in the question), the respective values would be:

a = 1

b = 3

c = - 4

Now, conditions to determine the nature.

If   0, the equation has real roots.

If    <  0, the equation has no real roots.

If    >  0, the equation has real and distinct roots.

Let's now solve the discriminant of the given equation.

From the given equation,

Using the values we mentioned above,

Since the discriminant (D) appears to be more than 0, the equation has real and distinct roots.