Which option correctly describes the nature of the roots of the quadratic equation \(7x^2-2x+5=0\)?
Answer and explanation
Correct answer: No real roots \(D=-136\)
Here, \(a=7\), \(b=-2\), and \(c=5\). Therefore, the discriminant is \(D=b^2-4ac=(-2)^2-4(7)(5)=4-140=-136\). Since \(D<0\), the equation has no real roots. Option C results from taking the sign of the discriminant incorrectly. In an exam, calculate \(D\) first and then check its sign to determine the nature of the roots.
Frequently asked questions
What is the correct answer to this question?
No real roots \(D=-136\)
Why is this the correct answer?
Here, \(a=7\), \(b=-2\), and \(c=5\). Therefore, the discriminant is \(D=b^2-4ac=(-2)^2-4(7)(5)=4-140=-136\). Since \(D<0\), the equation has no real roots. Option C results from taking the sign of the discriminant incorrectly. In an exam, calculate \(D\) first and then check its sign to determine the nature of the 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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