What is the nature of the roots of the equation \(4x^2-4x+3=0\)?
Answer and explanation
Correct answer: No real roots
Here, \(a=4\), \(b=-4\), and \(c=3\). The discriminant is \(\Delta=b^2-4ac=(-4)^2-4(4)(3)=16-48=-32<0\). Therefore, the equation has no real roots. Option D is incorrect because irrational and distinct roots are real roots and require a positive discriminant. Exam tip: For a quadratic equation, \(\Delta<0\) means that it has no real roots.
Frequently asked questions
What is the correct answer to this question?
No real roots
Why is this the correct answer?
Here, \(a=4\), \(b=-4\), and \(c=3\). The discriminant is \(\Delta=b^2-4ac=(-4)^2-4(4)(3)=16-48=-32<0\). Therefore, the equation has no real roots. Option D is incorrect because irrational and distinct roots are real roots and require a positive discriminant. Exam tip: For a quadratic equation, \(\Delta<0\) means that it has no real roots.
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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