Choose the correct statement about the nature of the roots of the equation \(x^2-10x+25=0\).
Answer and explanation
Correct answer: \(D=0\) and the roots are equal
Here, \(a=1, b=-10, c=25\). Therefore, the discriminant is \(D=b^2-4ac=(-10)^2-4(1)(25)=100-100=0\). Hence the roots are real and equal; in fact, the equation becomes \((x-5)^2=0\), giving the repeated root \(x=5\). Option B is incorrect because distinct real roots require \(D>0\). Exam tip: In a quadratic equation, \(D=0\) indicates equal roots immediately.
Frequently asked questions
What is the correct answer to this question?
\(D=0\) and the roots are equal
Why is this the correct answer?
Here, \(a=1, b=-10, c=25\). Therefore, the discriminant is \(D=b^2-4ac=(-10)^2-4(1)(25)=100-100=0\). Hence the roots are real and equal; in fact, the equation becomes \((x-5)^2=0\), giving the repeated root \(x=5\). Option B is incorrect because distinct real roots require \(D>0\). Exam tip: In a quadratic equation, \(D=0\) indicates equal roots immediately.
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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