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Class 10MathematicsPolynomialsGeometrical meaning of the zeroes of a polynomial.HardLevel 23
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If (p(x)=(x+3)^2(x-5)^2), how will the graph behave with the (x)-axis?

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Answer and explanation

Correct answer: It will touch at both zeroes

Both factors have even powers, so the graph touches at both places. Tip: an even-power zero usually gives touching, not crossing.

Related tags

Even MultiplicityTangentZeroes

Frequently asked questions

What is the correct answer to this question?

It will touch at both zeroes

Why is this the correct answer?

Both factors have even powers, so the graph touches at both places. Tip: an even-power zero usually gives touching, not crossing.

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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10 more MCQs
  1. 1What does a zero of a polynomial (p(x)) represent geometrically?
  2. 2If the graph of a polynomial cuts the x-axis at x = 3, what is its zero?
  3. 3If a graph cuts the (x)-axis at ((-2,0)) and ((4,0)), what are the zeroes of the polynomial?
  4. 4If the graph of a linear polynomial cuts the (x)-axis only once, how many zeroes will it have?
  5. 5From which point can the zero of a polynomial be directly found?
  6. 6If the graph of a polynomial neither cuts nor touches the (x)-axis, how many real zeroes does it have?
  7. 7If a parabola cuts the (x)-axis at two distinct points, how many zeroes does the quadratic polynomial have?
  8. 8If a parabola only touches the (x)-axis and does not cut it, how many real zeroes does the quadratic polynomial have?
  9. 9If a parabola lies completely above the (x)-axis, how many real zeroes does the quadratic polynomial have?
  10. 10Which points on the graph indicate the zeros (roots) of a polynomial \\(p(x)\\)?
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