Are the following statements 'True' or 'False'? Justify your answers.
If the graph of a polynomial intersects the $x$-axis at only one point,it cannot be a quadratic polynomial.
If the graph of a polynomial intersects the $x$-axis at only one point,it cannot be a quadratic polynomial.
(B) The statement is 'False'.
$A$ quadratic polynomial $p(x) = ax^2 + bx + c$ can intersect or touch the $x$-axis at only one point if the discriminant $D = b^2 - 4ac$ is equal to $0$.
In this case,the quadratic polynomial has two equal real roots,and the graph touches the $x$-axis at exactly one point (the vertex).
Therefore,a quadratic polynomial can indeed intersect the $x$-axis at only one point.
$A$ quadratic polynomial $p(x) = ax^2 + bx + c$ can intersect or touch the $x$-axis at only one point if the discriminant $D = b^2 - 4ac$ is equal to $0$.
In this case,the quadratic polynomial has two equal real roots,and the graph touches the $x$-axis at exactly one point (the vertex).
Therefore,a quadratic polynomial can indeed intersect the $x$-axis at only one point.
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