Question

The graph of a 3rd degree polynomial is shown below. Use the Fundamental Theorem of Algebra to determine the number of real and imaginary zeros.

Answer 1

`\quad \huge \quad \quad \boxed{ \tt \:Answer }`

`\qquad \tt \rightarrow \:\texttt{real roots : 2 }`

`\qquad \tt \rightarrow \: imaginary \: \: roots = 1`

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`\large \tt Solution \: :`

The given polynomial is a 3rd degree polynomial so it has a total of three roots.

And we know, where the curve (of polynomial) cuts the x - axis is its real root. so, from the graph we can infer that the given polynomial has 2 real roots [ as it cuts the x - axis at two points, i.e x = -2 and x = 1 ]

Hence, Number of real roots = 2

Number of imaginary roots = total roots - real roots

i.e 3 - 2 = 1

So, number of imaginary roots = 1

Answered by : ❝ AǫᴜᴀWɪᴢ ❞