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  • Are the following statements ‘True’ or ‘False’? Justify your answers. If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial.

Are the following statements ‘True’ or ‘False’? Justify your answers. If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial.

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Answer.          [True]

Polynomial : It is an expression of more than two algebraic terms, especially then sum of several terms that contains different powers of the same variable(s).

Quadratic polynomial : when the degree of polynomial is two then the polynomial is called quadratic polynomial.

Let us take an example :-

(x -1)^2 (x -2) = 0

It is a cubic polynomial

If we find its roots then x = 1, 2

Hence, there are only 2 roots of cubic polynomial (x -1)^2 (x -2) = 0 exist.

In other words we can say that the graph of this cubic polynomial intersect x-axis at two points x = 1, 2.

Hence we can say that if the graph of a polynomial intersect the x-axis at exactly two points, it need not to be a quadratic polynomial it may be a polynomial of higher degree.

Hence the given statement is true.

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