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If the quadratic equation \(px^2-18x+9=0\) has equal roots and \(p\neq 0\), what is the value of \(p\)?
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Answer and explanation
Correct answer: 9
For equal roots, the discriminant must be zero: \(D=b^2-4ac=0\). Here, \(a=p\), \(b=-18\), and \(c=9\), so \((-18)^2-4(p)(9)=0\), giving \(324-36p=0\) and hence \(p=9\). Exam tip: For equal roots, immediately apply the condition \(D=0\).
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
For equal roots, the discriminant must be zero: \(D=b^2-4ac=0\). Here, \(a=p\), \(b=-18\), and \(c=9\), so \((-18)^2-4(p)(9)=0\), giving \(324-36p=0\) and hence \(p=9\). Exam tip: For equal roots, immediately apply the condition \(D=0\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
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