Question

x^2018+1947x^1950+15x^8+26x^6+2019 discuss the nature of roots

Answer 1

Answer:

Al the roots of P(x) are imaginary

Step-by-step explanation:

$\text{Let}P(x)=x^{2018}+1947x^{1950}+15x^8+26x^6+2019$

consider the signs coefficients of P(x)

+ + + + +

since the number of change of signs of P(x) is zero, P(x) has no positive real roots

consider the signs coefficients of P(-x)

+ + + + +

since the number of change of signs of P(-x) is zero, P(x) has no negative real roots

Also P(x) has constant term

$\implies\:$ zero is not a root of P(x)

Hence, all the roots of P(x) are imaginary(complex roots)