Answer the statement as true or false.?

If a complex number such as -5 + 2i is a solution of a quadratic equation, then its conjugate -5 - 2i cannot be a solution to that same quadratic equation.Answer the statement as true or false.?
False. In fact, the opposite is (almost) true: if the complex number is a solution to a quadratic with rational (or integer) coefficients, then its conjugate MUST be a root. (Of course, if the coefficients are complex, then it's all out the window; any two complex numbers could be the roots.)





This can be seen using the quadratic formula, which states that roots of Ax虏+Bx+C are given by


x = [-B 卤 鈭?B虏-4AC)] / 2A.





Notice that if a root is complex, it is because 鈭?B虏-4AC) is pure imaginary, i.e. B虏-4AC %26lt; 0. Thus, the complex roots will be


[ -B 卤 i鈭?4AC-B虏) ] /2A.





Notice that the two are conjugates of each other (via the 卤).


搂Answer the statement as true or false.?
FALSE.


equation x^2 + 10x + 29 = 0 has roots --5 卤 2i.
that is absolutely true





-If a complex number such as -5 + 2i is a solution of a quadratic equation, then its conjugate -5 - 2i cannot be a solution to that same quadratic equation.
False
Remember, complex solutions ALWAYS come in pairs. So in this case, the complex conjugate of -5+2i is -5-2i. So this means that these two complex numbers are the solution to the quadratic equation. So the answer is false.
false
賾False.It is another solution. example: x^2+x+1=0


answers:( -1+sqrt(3)i)/2


and (-1-sqrt(3)i)/2
true