How to find zeroes of the …

We have seen that a quadratic polynomial is of the form:

p(x):ax²+bx+c,a≠0,

We assume that a, b and c are real numbers. In general, this polynomial has two zeroes. For example, the polynomial p(x):x²−3x+2 has the zeroes x=1,2

.For some quadratic polynomials, the two zeroes might be equal. For example, the polynomialp(x):x²−4x+4

can be rewritten as p(x):(x−2)2. Thus, we can say that this polynomial has the two zeroes: x=2,2,

which happen to be identical.

There might also be quadratic polynomials which have no real zeroes. Consider the polynomial p(x):x²+1

. For no real value of x can this polynomial take zero value, which means that this has no real zeroes. Note that this does not mean that the polynomial does not have any zeroes. Of course this polynomial has (two) zeroes – however, those zeroes are just not real numbers.