Question

LEVEL-1
Find the zeros of each of the following quadratic polynomials and verify the
relationship between the zeros and their coefficients:
p(x)= x²+2 root2 x -6



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Answer 1

A “zero of a polynomial” is a value (a number) at which the polynomial evaluates to zero. For example, the polynomial [math]x^2–3x+2[/math] has [math]1[/math] and [math]2[/math] as its zeros. The zeros of a polynomial are commonly called its “roots”. Every polynomial has its own multiset (an unordered list) of zeros. In fact, a polynomial is uniquely defined by its zeros, up to scaling by a constant value.

The “zero polynomial” is a specific polynomial, written [math]0[/math]. All its coefficients are zero, and treated as a function it’s a constant function. We could write this polynomial as [math]0 + 0x + 0x^2 + 0x^3 + \ldots[/math] to emphasize that it is a polynomial, but it’s a little strange because its degree is undefined. (The constant 1 is also a polynomial, but it has degree zero— a “zero-degree polynomial” and the “zero polynomial” are different.)

The “zeros of the zero polynomial” are all numbers, since substituting any value in for [math]x[/math] results in the value zero.

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