Assertion: The quadratic equation \(7x^2-14x+7=0\) has equal roots. Reason: Its discriminant is \(D=0\). Choose the correct option.
Answer and explanation
Correct answer: Both the assertion and the reason are correct, and the reason correctly explains the assertion
Here, \(a=7\), \(b=-14\), and \(c=7\). Therefore, the discriminant is \(D=b^2-4ac=(-14)^2-4(7)(7)=196-196=0\). For a quadratic equation, \(D=0\) means that the two roots are real and equal. Hence, both the assertion and the reason are correct, and the reason correctly explains the assertion. Exam tip: Calculate \(D=b^2-4ac\) first to determine the nature of the roots.
Frequently asked questions
What is the correct answer to this question?
Both the assertion and the reason are correct, and the reason correctly explains the assertion
Why is this the correct answer?
Here, \(a=7\), \(b=-14\), and \(c=7\). Therefore, the discriminant is \(D=b^2-4ac=(-14)^2-4(7)(7)=196-196=0\). For a quadratic equation, \(D=0\) means that the two roots are real and equal. Hence, both the assertion and the reason are correct, and the reason correctly explains the assertion. Exam tip: Calculate \(D=b^2-4ac\) first 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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