The roots of the equation x^2 - 10x + 21 = 0 are: (2020)

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Question: The roots of the equation x^2 - 10x + 21 = 0 are: (2020)

Options:

Correct Answer: 3 and 7

Exam Year: 2020

Solution:

Factoring gives (x - 3)(x - 7) = 0, so the roots are 3 and 7.

The roots of the equation x^2 - 10x + 21 = 0 are: (2020)

The roots of the equation x^2 - 10x + 21 = 0 are: (2020)

Step 1: Start with the equation x^2 - 10x + 21 = 0.
Step 2: Look for two numbers that multiply to 21 (the last number) and add up to -10 (the middle number).
Step 3: The two numbers that work are -3 and -7 because -3 * -7 = 21 and -3 + -7 = -10.
Step 4: Rewrite the equation using these numbers: (x - 3)(x - 7) = 0.
Step 5: Set each factor equal to zero: x - 3 = 0 and x - 7 = 0.
Step 6: Solve for x in each equation: x = 3 and x = 7.
Step 7: The roots of the equation are 3 and 7.

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.