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.
If the graph of a polynomial intersects the $x$-axis at exactly two points,it need not be a quadratic polynomial.
(A) The statement is 'True'.
If the graph of a polynomial intersects the $x$-axis at exactly two points,it does not necessarily have to be a quadratic polynomial.
$A$ polynomial of degree $n > 2$ can also intersect the $x$-axis at exactly two points if it has two real roots and the remaining $(n-2)$ roots are imaginary (non-real complex roots).
For example,a polynomial of degree $4$ can have two real roots and two imaginary roots,resulting in a graph that crosses the $x$-axis at only two points.
If the graph of a polynomial intersects the $x$-axis at exactly two points,it does not necessarily have to be a quadratic polynomial.
$A$ polynomial of degree $n > 2$ can also intersect the $x$-axis at exactly two points if it has two real roots and the remaining $(n-2)$ roots are imaginary (non-real complex roots).
For example,a polynomial of degree $4$ can have two real roots and two imaginary roots,resulting in a graph that crosses the $x$-axis at only two points.
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