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Class 10MathematicsPolynomialsGeometrical meaning of the zeroes of a polynomial.ExpertLevel 22
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If (p(x)=(x+5)^3(x-2)^2), where will the graph cross and where will it touch?

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Answer and explanation

Correct answer: It crosses at (x=-5) and touches at (x=2)

An odd-power zero gives crossing and an even-power zero gives touching. Tip: identify graph behavior from the power of the factor.

Related tags

MultiplicityCrossingTouching

Frequently asked questions

What is the correct answer to this question?

It crosses at (x=-5) and touches at (x=2)

Why is this the correct answer?

An odd-power zero gives crossing and an even-power zero gives touching. Tip: identify graph behavior from the power of the factor.

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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