If the vertex of a quadratic polynomial graph lies on the x-axis, what is correct about its real zeroes?
Answer and explanation
Correct answer: Both real zeroes are equal.
The vertex is the turning point of a parabola. If this vertex lies on the x-axis, its y-coordinate is zero, so the parabola meets the x-axis exactly at its turning point. It does not cross the axis at two separate locations; instead, the contact represents a repeated root. Algebraically, the quadratic can be written in the form a(x − r)², so both real zeroes are r and r. Therefore option A is correct. Distinct real zeroes would place the vertex away from the axis and produce two crossings. No real zero would occur if the parabola stayed completely above or below the axis, and a quadratic cannot have three real zeroes.
Frequently asked questions
What is the correct answer to this question?
Both real zeroes are equal.
Why is this the correct answer?
The vertex is the turning point of a parabola. If this vertex lies on the x-axis, its y-coordinate is zero, so the parabola meets the x-axis exactly at its turning point. It does not cross the axis at two separate locations; instead, the contact represents a repeated root. Algebraically, the quadratic can be written in the form a(x − r)², so both real zeroes are r and r. Therefore option A is correct. Distinct real zeroes would place the vertex away from the axis and produce two crossings. No real zero would occur if the parabola stayed completely above or below the axis, and a quadratic cannot have three real zeroes.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Geometrical meaning of the zeroes of a polynomial..
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