Find the solution(s) to the quadratic equation x2−10x+24

To solve the quadratic equation \( x^2 - 10x + 24 = 0 \), we can factor the expression.

We are looking for two numbers that multiply to \( 24 \) (the constant term) and add to \( -10 \) (the coefficient of the linear term).

The numbers \( -4 \) and \( -6 \) meet these criteria:

\[
(-4) \times (-6) = 24
\]
\[
(-4) + (-6) = -10
\]

So we can factor the quadratic as:

\[
(x - 4)(x - 6) = 0
\]

Setting each factor equal to zero gives us:

\[
x - 4 = 0 \quad \Rightarrow \quad x = 4
\]
\[
x - 6 = 0 \quad \Rightarrow \quad x = 6
\]

Thus, the solutions to the equation \( x^2 - 10x + 24 = 0 \) are \( x = 4 \) and \( x = 6 \).

Among the provided options, the correct answer is:

**Both x=4 and x=6 are solutions.**