The following is an example of a polynomial with only one root:

x² + 6x + 9 = 0

(x² + 6x + (6/2)²) - (6/2)² + 9 = 0

(x + 3)² - 9 + 9 = 0

(x + 3) ² = 0

x + 3 = 0

x = -3, or the polynomial has only one root x = -3

But not all polynomials have roots. The following is an example of a polynomial with no root:

2x² - 6x + 8 = 0

(½)(2x²- 6x + 8) = (½)0

x² - 3x + 4 = 0

(x² - 3x + (-3/2)²) - (-3/2)² + 4 = 0

(x - 3/2)²- 9/4 + 4 = 0

(x - 3/2)² + 7/4 = 0

(x - 3/2)² = -7/4

Because a real number squared is greater than or equal to 0, that means (x - 3/2)² will always be greater than or equal to 0. Therefore, the answer can’t be -7/4, a negative number, and there are no real roots for this polynomial.