Question

Find all complex solutions (real and non-real). (Enter your answers as a comma-separated list.) x3 8x2 21x 20

Answer 1

Answer:

The answer is "non-real solution: "i-3 and -i-3" and real solution is -2".

Step-by-step explanation:

In the given equation there is some mistype error so, its correct equation can be defined as follows:

Given value:

$\bold{ f(x) = x^3+ 8x^2 +22x +20}$

use hit and trial method we put x value are -2:

 $f(-2) = (-2)^3+ 8(-2)^2 +22(-2) +20$

            $= -8 + 8 \times 4 +22 \times -2 +20\\\\= -8 + 32 -44 +20\\\\= -52 + 52\\\\=0$

So, the real solution to the equation is "-2".

In the above solution, we calculate the f(x) =-2 is its real solution. so, the calculation for non-real solution:

divide the value $x^3+8x^2+ 22x +20$ by ($x+2$):

Quotient: $x^2+6x+10$

Remainder: 0

$\to x^2+6x+10 \\\\compare \ with \ ax^2+bx+c: \\\\a= 1\\b= 6\\c=10\\\\\bold{Formula:}\\\\\to D= b^2-4ac$

        $= 6^2- 4 \times 1 \times 10\\\\ = 36- 40\\\\ = -4$

Formula for calculate non-real solution:

$\bold{\frac{-b\pm \sqrt{D}}{2}}$

non-real solution: "i-3 and -i-3"