If a parabola remains above the x-axis and does not intersect it, which statement is correct for the related quadratic equation?
Answer and explanation
Correct answer: It has no real roots (D < 0)
The roots of a quadratic equation are the x-coordinates where its graph meets the x-axis. If the parabola remains entirely above the x-axis and does not touch or cross it, there is no point with y = 0. Therefore the equation has no real roots. For a quadratic, the discriminant condition for no real roots is D = b² − 4ac < 0. A tangent parabola touches the x-axis once and corresponds to D = 0, so option B describes a different situation. Crossing the axis twice gives D > 0, which is option C. Also, D = 1 is not implied by the graph and would only be a particular positive perfect-square value. Hence option A is correct.
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What is the correct answer to this question?
It has no real roots (D < 0)
Why is this the correct answer?
The roots of a quadratic equation are the x-coordinates where its graph meets the x-axis. If the parabola remains entirely above the x-axis and does not touch or cross it, there is no point with y = 0. Therefore the equation has no real roots. For a quadratic, the discriminant condition for no real roots is D = b² − 4ac < 0. A tangent parabola touches the x-axis once and corresponds to D = 0, so option B describes a different situation. Crossing the axis twice gives D > 0, which is option C. Also, D = 1 is not implied by the graph and would only be a particular positive perfect-square value. Hence option A is correct.
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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