Question

Solve by inspection. Which two are solutions for x2−8x+12=0
?(2 points)
Responses

x=6
x is equal to 6

x=−2
x is equal to negative 2

x=2
x is equal to 2

x=−6

Answer 1

To solve the equation \(x^2 - 8x + 12 = 0\) by inspection, we can look for two numbers that multiply to \(12\) (the constant term) and add up to \(-8\) (the coefficient of the \(x\) term).

The factors of \(12\) that satisfy this are:
- \(2\) and \(6\) (since \(2 + 6 = 8\))
- \(-2\) and \(-6\) (since \(-2 + (-6) = -8\))

Thus, the solutions are \(x = 2\) and \(x = 6\). However, to account for the signs correctly, we realize the solutions derived from \(-2\) and \(-6\) imply:

The factors of the quadratic equation can be represented as:
\((x - 2)(x - 6) = 0\)

Thus, the correct solutions for \(x\) that solve the equation \(x^2 - 8x + 12 = 0\) are:
- \(x = 2\)
- \(x = 6\)

From your options, the correct solutions are:
- \(x = 2\)
- \(x = 6\)