Which equation has roots 2 and 5?
Answer and explanation
Correct answer: x² − 7x + 10 = 0
The governing construction is the equation formed from known roots. If α and β are the roots of a monic quadratic, its equation is (x − α)(x − β) = 0. Substituting α = 2 and β = 5 gives (x − 2)(x − 5) = 0. On expansion, x² − 5x − 2x + 10 = x² − 7x + 10, so the required equation is x² − 7x + 10 = 0, which is option A. The same result follows from Vieta’s relations: the sum of roots is 7, so the coefficient of x is −7, and the product is 10, so the constant term is 10. Option B has the wrong sign for the sum, option C has the wrong sum, and option D has incorrect signs and product.
Frequently asked questions
What is the correct answer to this question?
x² − 7x + 10 = 0
Why is this the correct answer?
The governing construction is the equation formed from known roots. If α and β are the roots of a monic quadratic, its equation is (x − α)(x − β) = 0. Substituting α = 2 and β = 5 gives (x − 2)(x − 5) = 0. On expansion, x² − 5x − 2x + 10 = x² − 7x + 10, so the required equation is x² − 7x + 10 = 0, which is option A. The same result follows from Vieta’s relations: the sum of roots is 7, so the coefficient of x is −7, and the product is 10, so the constant term is 10. Option B has the wrong sign for the sum, option C has the wrong sum, and option D has incorrect signs and product.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
