What is the nature of the roots of the equation \\(4x^2+4x+5=0\\)?
Answer and explanation
Correct answer: No real roots; \\(D=-64\\)
For a quadratic equation \\(ax^2+bx+c=0\\), the discriminant is \\(D=b^2-4ac\\). Here, \\(a=4,b=4,c=5\\), so \\(D=4^2-4(4)(5)=16-80=-64\\). Since \\(D<0\\), the equation has no real roots. The roots are real and equal only when \\(D=0\\), so option B is not correct. Exam tip: determine the nature of roots by checking the sign of the discriminant first.
Frequently asked questions
What is the correct answer to this question?
No real roots; \\(D=-64\\)
Why is this the correct answer?
For a quadratic equation \\(ax^2+bx+c=0\\), the discriminant is \\(D=b^2-4ac\\). Here, \\(a=4,b=4,c=5\\), so \\(D=4^2-4(4)(5)=16-80=-64\\). Since \\(D<0\\), the equation has no real roots. The roots are real and equal only when \\(D=0\\), so option B is not correct. Exam tip: determine the nature of roots by checking the sign of the discriminant first.
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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