If the difference between the roots of x² - 7x + q = 0 is 1, what is the value of q?
Answer and explanation
Correct answer: 12
For the quadratic equation x² - 7x + q = 0, let the roots be α and β. By the relationships between roots and coefficients, α + β = 7 and αβ = q. The difference is given as 1, so take α - β = 1; if the order is reversed, the absolute difference is still 1. Solving α + β = 7 and α - β = 1 gives 2α = 8, hence α = 4, and β = 3. Therefore q = αβ = 4 × 3 = 12. Equivalently, the discriminant is (α - β)² = 1, so 49 - 4q = 1, which also gives q = 12. The other options do not satisfy both the sum and the stated root difference.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
For the quadratic equation x² - 7x + q = 0, let the roots be α and β. By the relationships between roots and coefficients, α + β = 7 and αβ = q. The difference is given as 1, so take α - β = 1; if the order is reversed, the absolute difference is still 1. Solving α + β = 7 and α - β = 1 gives 2α = 8, hence α = 4, and β = 3. Therefore q = αβ = 4 × 3 = 12. Equivalently, the discriminant is (α - β)² = 1, so 49 - 4q = 1, which also gives q = 12. The other options do not satisfy both the sum and the stated root difference.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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