The equation \\(x^2+10x+k=0\\) has no real roots. What is the correct condition on \\(k\\)?
Answer and explanation
Correct answer: \\(k>25\\)
A quadratic equation has no real roots when its discriminant satisfies \\(D<0\\). Here, \\(D=b^2-4ac=10^2-4(1)(k)=100-4k\\). Thus, \\(100-4k<0\\), which gives \\(k>25\\). When \\(k=25\\), the discriminant is zero and the equation has one repeated real root, so that option is not correct. Exam tip: For “no real roots,” apply the condition \\(D<0\\).
Frequently asked questions
What is the correct answer to this question?
\\(k>25\\)
Why is this the correct answer?
A quadratic equation has no real roots when its discriminant satisfies \\(D<0\\). Here, \\(D=b^2-4ac=10^2-4(1)(k)=100-4k\\). Thus, \\(100-4k<0\\), which gives \\(k>25\\). When \\(k=25\\), the discriminant is zero and the equation has one repeated real root, so that option is not correct. Exam tip: For “no real roots,” apply the condition \\(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.
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