Solve the equation 0=x2−12x+20

Question

algebraically using any method. Provide the smaller-valued solution in the first response field and the larger-valued solution in the second response field.(1 point)
The solutions are x=
and x=
.

Answer 1

To solve the equation \( 0 = x^2 - 12x + 20 \) algebraically, we can use the quadratic formula:

\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} \]

Here, \( a = 1 \), \( b = -12 \), and \( c = 20 \).

1. Calculate the discriminant:

\[ b^2 - 4ac = (-12)^2 - 4(1)(20) = 144 - 80 = 64 \]

2. Now, use the quadratic formula:

\[ x = \frac{{12 \pm \sqrt{64}}}{2(1)} = \frac{{12 \pm 8}}{2} \]

3. Calculate the two solutions:

• For the positive root: \[ x = \frac{{12 + 8}}{2} = \frac{20}{2} = 10 \]

• For the negative root: \[ x = \frac{{12 - 8}}{2} = \frac{4}{2} = 2 \]

The smaller-valued solution is \( 2 \) and the larger-valued solution is \( 10 \).

Smaller-valued solution: 2

Larger-valued solution: 10