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Q.

State whether the following statement is true or false.


A polynomial cannot be a quadratic polynomial if its graph only crosses the x-axis once.


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a

True

b

False 

answer is B.

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Detailed Solution

We know that, the curve that intersects the x-axis at only one point means that the roots of the quadratic equation are equal and coincide on the curve.
So, it is possible that the curve of the quadratic equation intersects at one point only.
But it can be linear, quadratic, or cubic polynomial.
Then, if the graph of a polynomial intersects the x-axis at only one point, it can be a linear, quadratic or cubic polynomial.
Therefore, the statement is false.
Hence, option (2) is correct.
 
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