If the quadratic equation \(px^2-14x+7=0\) has equal roots and \(p\ne0\), what is the value of \(p\)?
Answer and explanation
Correct answer: 7
For equal roots, the discriminant of a quadratic equation must be zero. Here, \(a=p\), \(b=-14\), and \(c=7\). Thus, \(b^2-4ac=0\) gives \((-14)^2-4(p)(7)=0\), so \(196-28p=0\) and \(p=7\). Therefore, option A is correct. Exam tip: For equal roots, directly use \(b^2-4ac=0\). Choosing 14 does not make the discriminant zero.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
For equal roots, the discriminant of a quadratic equation must be zero. Here, \(a=p\), \(b=-14\), and \(c=7\). Thus, \(b^2-4ac=0\) gives \((-14)^2-4(p)(7)=0\), so \(196-28p=0\) and \(p=7\). Therefore, option A is correct. Exam tip: For equal roots, directly use \(b^2-4ac=0\). Choosing 14 does not make the discriminant zero.
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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