If the quadratic equation \(2x^2+px+8=0\) has real and equal roots, what are the possible values of \(p\)?
Answer and explanation
Correct answer: \(p=\pm 8\)
For a quadratic equation \(ax^2+bx+c=0\) to have real and equal roots, its discriminant must be zero: \(D=b^2-4ac=0\). Here, \(a=2\), \(b=p\), and \(c=8\). Thus, \(p^2-4(2)(8)=0\), so \(p^2=64\) and \(p=\pm 8\). Therefore, option A is correct. Exam tip: when taking the square root of \(p^2=64\), include both the positive and negative values; hence option C is incomplete.
Frequently asked questions
What is the correct answer to this question?
\(p=\pm 8\)
Why is this the correct answer?
For a quadratic equation \(ax^2+bx+c=0\) to have real and equal roots, its discriminant must be zero: \(D=b^2-4ac=0\). Here, \(a=2\), \(b=p\), and \(c=8\). Thus, \(p^2-4(2)(8)=0\), so \(p^2=64\) and \(p=\pm 8\). Therefore, option A is correct. Exam tip: when taking the square root of \(p^2=64\), include both the positive and negative values; hence option C is incomplete.
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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