If the graph of a quadratic equation touches the x-axis at exactly one point, what is the nature of its roots?
Answer and explanation
Correct answer: Two real and equal roots (D=0)
When a parabola touches the x-axis at exactly one point, the quadratic has one repeated real root. Hence, the discriminant (D=b^2-4ac=0), and the two roots are real and equal. If (D>0), the graph cuts the x-axis at two points, so option B is incorrect. Exam tip: touching means (D=0), cutting means (D>0), and staying away means (D<0).
Frequently asked questions
What is the correct answer to this question?
Two real and equal roots (D=0)
Why is this the correct answer?
When a parabola touches the x-axis at exactly one point, the quadratic has one repeated real root. Hence, the discriminant (D=b^2-4ac=0), and the two roots are real and equal. If (D>0), the graph cuts the x-axis at two points, so option B is incorrect. Exam tip: touching means (D=0), cutting means (D>0), and staying away means (D<0).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
