To solve the problem, we begin by substituting the given values [tex]\( A = 1,000,000 \)[/tex], [tex]\( P = 10,000 \)[/tex], and [tex]\( T = 2 \)[/tex] into the formula [tex]\( A = P(1 + r)^T \)[/tex].
Substitute these values into the formula:
[tex]\[ 1,000,000 = 10,000 (1 + r)^2 \][/tex]
Next, we need to isolate the term [tex]\( (1 + r)^2 \)[/tex]. To do this, divide both sides of the equation by [tex]\( 10,000 \)[/tex]:
[tex]\[ \frac{1,000,000}{10,000} = (1 + r)^2 \][/tex]
[tex]\[ 100 = (1 + r)^2 \][/tex]
Now, let's express this equation as a quadratic equation. Rewrite [tex]\( (1 + r)^2 \)[/tex]:
[tex]\[ (1 + r)^2 = 100 \][/tex]
Expanding [tex]\( (1 + r)^2 \)[/tex], we get:
[tex]\[ 1 + 2r + r^2 = 100 \][/tex]
Subtract 100 from both sides to set the equation to zero:
[tex]\[ r^2 + 2r + 1 - 100 = 0 \][/tex]
Simplify:
[tex]\[ r^2 + 2r - 99 = 0 \][/tex]
Thus, the quadratic equation is:
[tex]\[ r^2 + 2r - 99 = 0 \][/tex]
