Question

Which statement about the zeros of a quadratic polynomial is true?

1.
There must be one complex zero, not just real zeros.
2.
If the polynomial is quadratic, then it can have a maximum of 2 zeros, not 3.
3.
If−4
and 3 are zeros, the conjugates 4 and−3
must also be zeros.
4.
If the quadratic polynomial has 3 zeros, then it must have complex coefficients.

Answer 1

The answer is 2.

If the polynomial is quadratic, then it can have a maximum of 2 zeros, not 3.

Since we are talking about quadratic expressions of the form

ax² +bx +c = 0 , with a,b,c ≠0

There are only two possible solutions

x1 = [-b + sqrt(b² -4a*c)]/(2*a)

x2 = [-b - sqrt(b² -4a*c)]/(2*a)