Question

check whether x^2+6x+15 has zeroes or not​

Answer 1

Answer:

There are no real zeros for the equation.But the imaginary zeros are, -6+$\sqrt{6}$ i and  -6-

Step-by-step explanation:

Let me use the Quadratic equation formula,which is used to find zeros.

-b±$\frac{\sqrt{b^{2}-4ac } }{2a}$ ,where the polynomial is ax²+bx+c

From the polynomial,

a=1;b=6;c=15

Sub. these values in the formula,

-6±$\frac{\sqrt{36-4(1)(15)} }{2(1)}$ ---> (1)

but,consider the square root term.The square root term is

36-4(1)(15),which is,-24..

So,$\sqrt{-24}$ doesn't exist.

So,the polynomial has no real zeros.

But still,it has imaginary zeros.

Solving the leftover equation (1) further,

-6±$\frac{\sqrt{(24)(-1)}} {2}$

= -6 ± $\sqrt{(6)(-1)}$

= -6±$\sqrt{6}$  i       [i = $\sqrt{-1}$]

The roots of the polynomial equation are -6+$\sqrt{6}$  i  and -6-