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A student says that the equation \(x^2-2x+5=0\) has two real roots because \(b^2\) is positive. What is the correct evaluation of this statement?
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Answer and explanation
Correct answer: The student has misunderstood the discriminant; \(D=-16<0\), so there are no real roots.
Here \(a=1, b=-2, c=5\), so \(D=b^2-4ac=4-20=-16\). A negative discriminant means there are no real roots. In exams, evaluate the complete \(b^2-4ac\), not \(b^2\) alone.
Frequently asked questions
What is the correct answer to this question?
The student has misunderstood the discriminant; \(D=-16<0\), so there are no real roots.
Why is this the correct answer?
Here \(a=1, b=-2, c=5\), so \(D=b^2-4ac=4-20=-16\). A negative discriminant means there are no real roots. In exams, evaluate the complete \(b^2-4ac\), not \(b^2\) alone.
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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