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# AMC 8 2019 Problem 20 | Fundamental Theorem of Algebra

Try out this beautiful algebra problem number 2 from AMC 8 2019 based on the Fundamental Theorem of Algebra.

## AMC 8 2019 Problem 20:

How many different real numbers  satisfy the equation

$\textbf{(A) }0$
$\textbf{(B) }1$
$\textbf{(C) }2$
$\textbf{(D) }4$
$\textbf{(E) }8$

### Key Concepts

Algebra

Value

Telescoping

AMC 8, 2019, Problem 20

## Try with Hints

1st Hint

The given equation is

and that means

2nd Hint

Among both cases, if

then,

and that means we have 2 different real numbers that satisfy the equation.

Final Step

and if we take another case, then

and so,

and that means we have 2 different real numbers in this case too that satisfy the equation. So total 2+2=4 real numbers that satisfy the equation.

Cheenta Numerates Program for AMC - AIME

### Subscribe to Cheenta at Youtube

Try out this beautiful algebra problem number 2 from AMC 8 2019 based on the Fundamental Theorem of Algebra.

## AMC 8 2019 Problem 20:

How many different real numbers  satisfy the equation

$\textbf{(A) }0$
$\textbf{(B) }1$
$\textbf{(C) }2$
$\textbf{(D) }4$
$\textbf{(E) }8$

### Key Concepts

Algebra

Value

Telescoping

AMC 8, 2019, Problem 20

## Try with Hints

1st Hint

The given equation is

and that means

2nd Hint

Among both cases, if

then,

and that means we have 2 different real numbers that satisfy the equation.

Final Step

and if we take another case, then

and so,

and that means we have 2 different real numbers in this case too that satisfy the equation. So total 2+2=4 real numbers that satisfy the equation.

Cheenta Numerates Program for AMC - AIME

### Subscribe to Cheenta at Youtube

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