The difference between the two roots of the equation \(x^2+6x+r=0\) is \(2\sqrt{5}\). What is the value of \(r\)?
Answer and explanation
Correct answer: 4
Let the roots be \(\alpha\) and \(\beta\). Then \(\alpha+\beta=-6\) and \(\alpha\beta=r\). Using \((\alpha-\beta)^2=(\alpha+\beta)^2-4\alpha\beta\), we get \(20=36-4r\), so \(r=4\). Exam tip: Square the difference of the roots and relate it to their sum and product; the sign of the sum does not affect its square.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Let the roots be \(\alpha\) and \(\beta\). Then \(\alpha+\beta=-6\) and \(\alpha\beta=r\). Using \((\alpha-\beta)^2=(\alpha+\beta)^2-4\alpha\beta\), we get \(20=36-4r\), so \(r=4\). Exam tip: Square the difference of the roots and relate it to their sum and product; the sign of the sum does not affect its square.
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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