If the sum of the roots of a quadratic equation is 7 and their product is 10, which is its monic quadratic equation?
Answer and explanation
Correct answer: \(x^2-7x+10=0\)
If the roots are \(\alpha\) and \(\beta\), the monic quadratic equation is \(x^2-(\alpha+\beta)x+\alpha\beta=0\). Substituting \(\alpha+\beta=7\) and \(\alpha\beta=10\) gives \(x^2-7x+10=0\). Option A has the wrong sign for the sum, while option B interchanges the sum and product. Exam tip: in the monic form, the coefficient of \(x\) is the negative of the sum of roots, and the constant term is their product.
Frequently asked questions
What is the correct answer to this question?
\(x^2-7x+10=0\)
Why is this the correct answer?
If the roots are \(\alpha\) and \(\beta\), the monic quadratic equation is \(x^2-(\alpha+\beta)x+\alpha\beta=0\). Substituting \(\alpha+\beta=7\) and \(\alpha\beta=10\) gives \(x^2-7x+10=0\). Option A has the wrong sign for the sum, while option B interchanges the sum and product. Exam tip: in the monic form, the coefficient of \(x\) is the negative of the sum of roots, and the constant term is their 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.
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