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Which quadratic equation will have two distinct real roots?
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Answer and explanation
Correct answer: \(2x^2-5x+2=0\)
For \(ax^2+bx+c=0\), two distinct real roots require the discriminant \(D=b^2-4ac>0\). In option C, \(D=(-5)^2-4\cdot2\cdot2=9>0\). Option A has \(D=0\), so its roots are equal. Exam tip: check the sign of \(D\) first.
Frequently asked questions
What is the correct answer to this question?
\(2x^2-5x+2=0\)
Why is this the correct answer?
For \(ax^2+bx+c=0\), two distinct real roots require the discriminant \(D=b^2-4ac>0\). In option C, \(D=(-5)^2-4\cdot2\cdot2=9>0\). Option A has \(D=0\), so its roots are equal. Exam tip: check the sign of \(D\) 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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