What is the nature of the roots of the quadratic equation \(4x^2-12x+9=0\)?
Answer and explanation
Correct answer: Two real and equal
Here, \(a=4\), \(b=-12\), and \(c=9\). The discriminant is \(D=b^2-4ac=(-12)^2-4(4)(9)=144-144=0\). Therefore, the roots are real and equal. In fact, \(4x^2-12x+9=(2x-3)^2\), so both roots are \(x=\frac{3}{2}\). Exam tip: When \(D=0\), the roots are always real and equal.
Frequently asked questions
What is the correct answer to this question?
Two real and equal
Why is this the correct answer?
Here, \(a=4\), \(b=-12\), and \(c=9\). The discriminant is \(D=b^2-4ac=(-12)^2-4(4)(9)=144-144=0\). Therefore, the roots are real and equal. In fact, \(4x^2-12x+9=(2x-3)^2\), so both roots are \(x=\frac{3}{2}\). Exam tip: When \(D=0\), the roots are always real and equal.
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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