Question: The sum of the roots of the equation x^2 - 7x + 10 = 0 is?
Options:
5
6
7
8
Correct Answer: 7
Solution:
The sum of the roots is given by -b/a = 7/1 = 7.
The sum of the roots of the equation x^2 - 7x + 10 = 0 is?
Practice Questions
Q1
The sum of the roots of the equation x^2 - 7x + 10 = 0 is?
5
6
7
8
Questions & Step-by-Step Solutions
The sum of the roots of the equation x^2 - 7x + 10 = 0 is?
Step 1: Identify the coefficients in the quadratic equation x^2 - 7x + 10 = 0. Here, a = 1, b = -7, and c = 10.
Step 2: Use the formula for the sum of the roots of a quadratic equation, which is -b/a.
Step 3: Substitute the value of b into the formula. Since b = -7, we have -(-7)/1.
Step 4: Simplify the expression. This becomes 7/1.
Step 5: Calculate the result. 7/1 equals 7.
Step 6: Conclude that the sum of the roots is 7.
Quadratic Equations – Understanding the properties of quadratic equations, specifically the relationship between coefficients and the sum of the roots.
Vieta's Formulas – Application of Vieta's formulas which state that for a quadratic equation ax^2 + bx + c = 0, the sum of the roots is -b/a.
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