If the equation \(kx^2-18x+81=0\) has equal roots, what is the value of \(k\)?
Answer and explanation
Correct answer: 1
A quadratic equation \(ax^2+bx+c=0\) has equal roots when its discriminant \(b^2-4ac\) is zero. Here, \(a=k\), \(b=-18\), and \(c=81\). Thus, \((-18)^2-4(k)(81)=0\), giving \(324-324k=0\) and hence \(k=1\). Exam tip: identify the coefficient of \(x^2\) as \(a\) before applying the discriminant formula.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
A quadratic equation \(ax^2+bx+c=0\) has equal roots when its discriminant \(b^2-4ac\) is zero. Here, \(a=k\), \(b=-18\), and \(c=81\). Thus, \((-18)^2-4(k)(81)=0\), giving \(324-324k=0\) and hence \(k=1\). Exam tip: identify the coefficient of \(x^2\) as \(a\) before applying the discriminant formula.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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