If the equation \\(qx^2+5x+q=0\\) has equal roots and \\(q\\ne 0\\), what are the possible values of \\(q\\)?
Answer and explanation
Correct answer: \\(q=\\frac{5}{2}\\) or \\(q=-\\frac{5}{2}\\)
For equal roots, the discriminant \\(D=b^2-4ac\\) must be zero. Here, \\(a=q\\), \\(b=5\\), and \\(c=q\\), so \\(D=25-4q^2=0\\). Thus, \\(q^2=\\frac{25}{4}\\), giving \\(q=\\pm\\frac{5}{2}\\). The values \\(5\\) and \\(-5\\) in option B do not make the discriminant zero. Also, \\(q=0\\) is excluded because it would make the equation non-quadratic. Exam tip: for equal roots, set the discriminant directly equal to zero.
Frequently asked questions
What is the correct answer to this question?
\\(q=\\frac{5}{2}\\) or \\(q=-\\frac{5}{2}\\)
Why is this the correct answer?
For equal roots, the discriminant \\(D=b^2-4ac\\) must be zero. Here, \\(a=q\\), \\(b=5\\), and \\(c=q\\), so \\(D=25-4q^2=0\\). Thus, \\(q^2=\\frac{25}{4}\\), giving \\(q=\\pm\\frac{5}{2}\\). The values \\(5\\) and \\(-5\\) in option B do not make the discriminant zero. Also, \\(q=0\\) is excluded because it would make the equation non-quadratic. Exam tip: for equal roots, set the discriminant directly equal to 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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