Which of the following quadratic equations has two real and equal roots?
Answer and explanation
Correct answer: \(x^2-6x+9=0\)
A quadratic equation \(ax^2+bx+c=0\) has two real and equal roots when its discriminant \(D=b^2-4ac\) is zero. For option (A), \(a=1, b=-6, c=9\), so \(D=(-6)^2-4(1)(9)=36-36=0\). Hence its roots are equal, namely \(x=3,3\). Options (B) and (D) have discriminants 4 and 16, respectively, so their roots are distinct; option (C) has discriminant \(-4\), so its roots are not real. Exam tip: For equal roots, check directly whether \(D=0\).
Frequently asked questions
What is the correct answer to this question?
\(x^2-6x+9=0\)
Why is this the correct answer?
A quadratic equation \(ax^2+bx+c=0\) has two real and equal roots when its discriminant \(D=b^2-4ac\) is zero. For option (A), \(a=1, b=-6, c=9\), so \(D=(-6)^2-4(1)(9)=36-36=0\). Hence its roots are equal, namely \(x=3,3\). Options (B) and (D) have discriminants 4 and 16, respectively, so their roots are distinct; option (C) has discriminant \(-4\), so its roots are not real. Exam tip: For equal roots, check directly whether \(D=0\).
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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