The equation x3 + 3x2 + 5x + 15 = 0 has real and imaginary solution(s).

Given Equation has 1 real Solution and 2 Imaginary Solution.  

Real Solution of given Equation is -3 and Imaginary solution are .

Step-by-step explanation:

Given Equation : x³ + 3x² + 5x + 15 = 0

let p(x) =  x³ + 3x² + 5x + 15

From polynomial factor theorem,

put x = -3

p(-3) = (-3)³ + 3(-3)² + 5(-3) + 15

        = -27 + 27 - 15 + 15

       = 0

So, -3 is one of the zero of the polynomial and solution of the equation.

Also, x + 3 is factor of p(x)

We get another factor by dividing p(x) by x + 3

that is x² + 5

so, to get other solution of given equation we put this factor equal to 0

x² + 5 = 0

x² = -5

x = ± √-5

x = + √5 × √-1 and   x = - √5 ×√-1

Therefore, Given Equation has 1 real Solution and 2 Imaginary Solution.  

Real Solution of given Equation is -3 and Imaginary solution are .

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

what's the question?

step-by-step explanation:

there is no question.