If the parabola representing a quadratic equation neither intersects nor touches the x-axis, what can be concluded about its real roots?
Answer and explanation
Correct answer: No real roots, \(D<0\)
The points where the parabola intersects the x-axis represent the real roots of the quadratic equation. If it neither intersects nor touches the x-axis, there is no real intercept; therefore, the discriminant satisfies \(D<0\), and the equation has no real roots. In contrast, touching the x-axis would give \(D=0\).
Frequently asked questions
What is the correct answer to this question?
No real roots, \(D<0\)
Why is this the correct answer?
The points where the parabola intersects the x-axis represent the real roots of the quadratic equation. If it neither intersects nor touches the x-axis, there is no real intercept; therefore, the discriminant satisfies \(D<0\), and the equation has no real roots. In contrast, touching the x-axis would give \(D=0\).
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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