Which of the following quadratic equations has equal roots?
Answer and explanation
Correct answer: \(7x^2-10\sqrt{7}x+25=0\)
For a quadratic equation \(ax^2+bx+c=0\), equal roots occur if and only if the discriminant \(D=b^2-4ac\) is zero. In option A, \(a=7\), \(b=-10\sqrt{7}\), and \(c=25\), so \(D=(-10\sqrt{7})^2-4(7)(25)=700-700=0\). Hence, its two roots are equal. For instance, option B has \(D=(-9\sqrt{7})^2-700=-133\), so it does not have real roots. Exam tip: To identify equal roots, check \(D=0\) directly instead of using the full quadratic formula.
Frequently asked questions
What is the correct answer to this question?
\(7x^2-10\sqrt{7}x+25=0\)
Why is this the correct answer?
For a quadratic equation \(ax^2+bx+c=0\), equal roots occur if and only if the discriminant \(D=b^2-4ac\) is zero. In option A, \(a=7\), \(b=-10\sqrt{7}\), and \(c=25\), so \(D=(-10\sqrt{7})^2-4(7)(25)=700-700=0\). Hence, its two roots are equal. For instance, option B has \(D=(-9\sqrt{7})^2-700=-133\), so it does not have real roots. Exam tip: To identify equal roots, check \(D=0\) directly instead of using the full quadratic formula.
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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