If \(p\) is a real number, what is the condition for the equation \(x^2+2px+25=0\) to have real roots?
Answer and explanation
Correct answer: \(p\leq -5\) या \(p\geq 5\)
A quadratic equation has real roots when its discriminant satisfies \(D\geq 0\). Here, \(a=1\), \(b=2p\), and \(c=25\), so \(D=(2p)^2-4(1)(25)=4p^2-100\). Thus, \(4p^2-100\geq 0\), which gives \(p^2\geq 25\), and hence \(p\leq -5\) or \(p\geq 5\). Option B reverses the required inequality and also excludes the double real roots occurring at \(p=\pm5\). Exam tip: For real roots, use \(D\geq0\), not only \(D>0\).
Frequently asked questions
What is the correct answer to this question?
\(p\leq -5\) या \(p\geq 5\)
Why is this the correct answer?
A quadratic equation has real roots when its discriminant satisfies \(D\geq 0\). Here, \(a=1\), \(b=2p\), and \(c=25\), so \(D=(2p)^2-4(1)(25)=4p^2-100\). Thus, \(4p^2-100\geq 0\), which gives \(p^2\geq 25\), and hence \(p\leq -5\) or \(p\geq 5\). Option B reverses the required inequality and also excludes the double real roots occurring at \(p=\pm5\). Exam tip: For real roots, use \(D\geq0\), not only \(D>0\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
