The quadratic polynomial have zeroes
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a quadratic polynomial (we assume that the coefficients are real) will always have two zeroes, but the nature of the zeroes depends on the coefficients: The two zeroes might be real and distinct. The two zeroes might be real and identical. The two zeroes might not be real numbers.
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Zeroes of a quadratic polynomial
If p ( x ) = x 2 − 12 x + 35 is a polynomial, then a zero of is a number with the property that p ( r ) = 0 .
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A simple example of a quadratic polynomial with no real zeroes is x^2 + 1 which has roots \pm i where i represents \sqrt{-1}. An example of a polynomial with one real root is x^2 which has only 0 as a root. And an example of a polynomial with two real roots is x^2 - 1, which has roots \pm 1.
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