The roots of the equation x^2 - 7x + 10 = 0 are: (2019)

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Question: The roots of the equation x^2 - 7x + 10 = 0 are: (2019)

Options:

Correct Answer: 3 and 4

Exam Year: 2019

Solution:

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

The roots of the equation x^2 - 7x + 10 = 0 are: (2019)

The roots of the equation x^2 - 7x + 10 = 0 are: (2019)

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 two numbers that work are -2 and -5 because -2 * -5 = 10 and -2 + -5 = -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.
Factoring – Recognizing how to factor a quadratic expression into two binomials.
Roots of Equations – Identifying the solutions (roots) of a quadratic equation.