Question

Which two values of x are the roots of the polynomial below?
x^2+5x+11

Answer 1

Answer: The roots of the given polynomial are

`x=(-5+i√(19))/(2),~~(-5-i√(19))/(2).`

Step-by-step explanation: We are given to find the two values of x that are the roots of the following quadratic polynomial:

`P(x)=x^2+5x+11.`

To find the roots, we must have

`P(x)=0\\\\\Rightarrow x^2+5x+11=0~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We know that

the solution set of quadratic equation of the form
`ax^2+bx+c=0,~a\\eq 0` is given by

`x=(-b\pm√(b^2-4ac))/(2a).`

From equation (i), we have

a = 1, b = 5 and c = 11.

Therefore, the solution of equation (i) is given by

`x\\\\\\=(-b\pm√(b^2-4ac))/(2a)\\\\\\=(-5\pm√(5^2-4*1* 11))/(2* 1)\\\\\\=(-5\pm√(25-44))/(2)\\\\\\=(-5\pm√(-19))/(2)\\\\\\=(-5\pm i√(19))/(2).`

Thus, the roots of the given polynomial are

`x=(-5+i√(19))/(2),~~(-5-i√(19))/(2).`