If the roots of the quadratic equation \(x^2-10x+k=0\) are distinct prime numbers, what is the value of \(k\)?
Answer and explanation
Correct answer: 21
By Vieta’s relations, the sum of the roots is \(10\) and their product is \(k\). The distinct prime numbers that sum to 10 are \(3\) and \(7\); the pair \(5,5\) is excluded because the roots must be distinct. Hence, \(k=3\times7=21\). Exam tip: In \(x^2-Sx+P=0\), the sum of the roots is \(S\) and their product is \(P\).
Frequently asked questions
What is the correct answer to this question?
21
Why is this the correct answer?
By Vieta’s relations, the sum of the roots is \(10\) and their product is \(k\). The distinct prime numbers that sum to 10 are \(3\) and \(7\); the pair \(5,5\) is excluded because the roots must be distinct. Hence, \(k=3\times7=21\). Exam tip: In \(x^2-Sx+P=0\), the sum of the roots is \(S\) and their product is \(P\).
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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