Axe199 said:
Ray Vickson said:
Axe199 said:
okay...thanks very much, tht was a tricky one, or maybe i am stupid :Dslider142 said:
The roots of a squared polynomial are the values of the variable that make the polynomial equal to zero. For example, the roots of the polynomial x^2 + 4x + 4 are -2 and -2, since (-2)^2 + 4(-2) + 4 = 0.
Yes, a squared polynomial can have complex roots. Complex numbers are numbers that include a real part and an imaginary part, such as 3 + 4i. If a polynomial has complex coefficients, it is possible for it to have complex roots as well.
To find the roots of a squared polynomial with complex numbers, you can use the quadratic formula. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the polynomial in the form ax^2 + bx + c. The ± sign indicates that there will be two solutions, one with a positive square root and one with a negative square root.
If the roots of a squared polynomial are imaginary, it means that the polynomial has no real roots. This can happen when the discriminant (b^2 - 4ac) in the quadratic formula is negative, resulting in a square root of a negative number. Imaginary roots are still valid solutions to the polynomial, but they will be complex numbers.
Yes, a polynomial with real coefficients can have complex roots. This can happen when the polynomial has a quadratic term with a coefficient that is not a perfect square. For example, the polynomial x^2 + 2x + 5 has complex roots, even though all of its coefficients are real numbers.
