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Explore the Back-StoryTry out this beautiful algebra problem number 2 from AMC 8 2019 based on the Fundamental Theorem of Algebra.

How many different real numbers satisfy the equation

$\textbf{(A) }0$

$\textbf{(B) }1$

$\textbf{(C) }2$

$\textbf{(D) }4$

$\textbf{(E) }8$

Algebra

Value

Telescoping

But try the problem first...

Answer: is (D) 4

Source

AMC 8, 2019, Problem 20

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

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

How many different real numbers satisfy the equation

$\textbf{(A) }0$

$\textbf{(B) }1$

$\textbf{(C) }2$

$\textbf{(D) }4$

$\textbf{(E) }8$

Algebra

Value

Telescoping

But try the problem first...

Answer: is (D) 4

Source

AMC 8, 2019, Problem 20

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

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