The sum of the roots of the equation x^2 - 7x + k = 0 is 7. What is the value of
Practice Questions
Q1
The sum of the roots of the equation x^2 - 7x + k = 0 is 7. What is the value of k if the product of the roots is 10? (2023)
10
15
20
25
Questions & Step-by-Step Solutions
The sum of the roots of the equation x^2 - 7x + k = 0 is 7. What is the value of k if the product of the roots is 10? (2023)
Step 1: Identify the equation given, which is x^2 - 7x + k = 0.
Step 2: Recall Vieta's formulas, which state that for a quadratic equation ax^2 + bx + c = 0, the sum of the roots (r1 + r2) is -b/a and the product of the roots (r1 * r2) is c/a.
Step 3: In our equation, a = 1, b = -7, and c = k.
Step 4: According to Vieta's formulas, the sum of the roots (r1 + r2) = -(-7)/1 = 7. This matches the information given in the question.
Step 5: Next, we know the product of the roots (r1 * r2) = k. The question states that this product is equal to 10.
