Analyzing and Factoring Quadratic Expression: x^2 – 10x + 24 – Step-by-Step Guide with Solutions

x^2 – 10x + 24

To analyze the expression x^2 – 10x + 24, we can rearrange it as a quadratic equation ax^2 + bx + c

To analyze the expression x^2 – 10x + 24, we can rearrange it as a quadratic equation ax^2 + bx + c. Comparing the two forms, we can determine that a = 1, b = -10, and c = 24.

This quadratic expression can be factored to find its roots or solutions. Let’s factor it:

To factor the quadratic expression, we need to find two numbers that multiply to give c (24) and add up to give b (-10).

The numbers that satisfy this condition are -4 and -6. When -4 and -6 are added, we get -10, and when they are multiplied, we get 24.

Using these values, we can rewrite the expression as (x – 4)(x – 6).

Therefore, the factored form of x^2 – 10x + 24 is (x – 4)(x – 6).

Additionally, we can find the x-intercepts or roots of the quadratic equation by setting it equal to zero:

(x – 4)(x – 6) = 0

To solve this equation, we set each factor equal to zero:

x – 4 = 0 or x – 6 = 0

Solving for x in each equation, we get:

x = 4 or x = 6

So, the roots of the quadratic equation are x = 4 and x = 6.

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