Question

find the nature of the roots of the following equation: 2x^5 + x^3 + 5x + 1

Answer 1

Step-by-step explanation:

nature of the roots of a given equation is above

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Answer 2

Given :

The quadratic equation is

2 $x^{5}$ + x³ + 5 x + 1 = 0

To Find :

The nature of roots of equation

Solution :

For any quadratic equation, the nature of roots is determined by finding its discriminant ;

Since Discriminant = D =  b² - 4 a c  , for the equation ax² + b x + c = 0

If The equation is of higher order, then roots can be determined in similar ways.

So, From given equation  2 $x^{5}$ + x³ + 5 x + 1 = 0

a =  2 , b = 1 , c = 5

∵   D =  b² - 4 a c  

Or,   D =  (1)² - 4 × 2 × 5

Or,   D = 1 - 40

Or,  D = - 39

i.e  D < 0

Now, The discriminant is negative so,

Fro D < 0  , The roots of equation is imaginary

Hence, The roots of given quadratic equation is imaginary . Answer