If the roots of the equation \(x^2-9x+c=0\) are in the ratio \(1:2\), what is the value of \(c\)?
Answer and explanation
Correct answer: 18
Let the roots be \(t\) and \(2t\). Their sum is \(9\), so \(t+2t=9\), giving \(t=3\). Hence, the roots are \(3\) and \(6\). The product of the roots equals \(c\), so \(c=3\times6=18\). Exam tip: In \(x^2+bx+c=0\), the sum of the roots is \(-b\) and their product is \(c\).
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
Let the roots be \(t\) and \(2t\). Their sum is \(9\), so \(t+2t=9\), giving \(t=3\). Hence, the roots are \(3\) and \(6\). The product of the roots equals \(c\), so \(c=3\times6=18\). Exam tip: In \(x^2+bx+c=0\), the sum of the roots is \(-b\) and their product is \(c\).
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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