Which statement correctly describes the nature of the roots of \(x^2-8x+17=0\)?
Answer and explanation
Correct answer: It has no real roots
Here, \(a=1\), \(b=-8\), and \(c=17\). Therefore, the discriminant is \(\Delta=b^2-4ac=(-8)^2-4(1)(17)=64-68=-4\). Since \(\Delta<0\), the equation has no real roots, so option A is correct. Option B would be correct only if \(\Delta=0\). Exam tip: \(\Delta<0\) means no real roots, \(\Delta=0\) means equal real roots, and \(\Delta>0\) means distinct real roots.
Frequently asked questions
What is the correct answer to this question?
It has no real roots
Why is this the correct answer?
Here, \(a=1\), \(b=-8\), and \(c=17\). Therefore, the discriminant is \(\Delta=b^2-4ac=(-8)^2-4(1)(17)=64-68=-4\). Since \(\Delta<0\), the equation has no real roots, so option A is correct. Option B would be correct only if \(\Delta=0\). Exam tip: \(\Delta<0\) means no real roots, \(\Delta=0\) means equal real roots, and \(\Delta>0\) means distinct real roots.
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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