The equation x^2 - 7x + 10 = 0 has roots that are:

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Question: The equation x^2 - 7x + 10 = 0 has roots that are:

Options:

Correct Answer: 3 and 4

Solution:

Factoring the equation gives (x - 2)(x - 5) = 0, so the roots are 2 and 5.

The equation x^2 - 7x + 10 = 0 has roots that are:

The equation x^2 - 7x + 10 = 0 has roots that are:

Step 1: Start with the equation x^2 - 7x + 10 = 0.
Step 2: Look for two numbers that multiply to 10 (the constant term) and add up to -7 (the coefficient of x).
Step 3: The numbers -2 and -5 multiply to 10 and add to -7.
Step 4: Rewrite the equation using these numbers: (x - 2)(x - 5) = 0.
Step 5: Set each factor equal to zero: x - 2 = 0 and x - 5 = 0.
Step 6: Solve for x in each equation: x = 2 and x = 5.
Step 7: The roots of the equation are 2 and 5.

Quadratic Equations – Understanding how to solve quadratic equations using factoring.
Roots of Equations – Identifying the roots of a quadratic equation from its factored form.