Is it complex conjugate?? But it is not in my syllabus, so have other ways to solve this problemHave you learned a theorem about complex roots of polynomials with real coefficients?
If not, there are several ways you might convince yourself in the case of a quadratic. Please either make an attempt, or just tell us what you have learned that might be useful. One such thing would be the quadratic formula; another could be the factor theorem.
Notation: suppose \(z=a+bi\) then the congregate is \(\overline{~z~}=a-bi\).Given a=3+7i is root of the quadratic equation X^2+px+q=0, where p and q are real numbers.
Sorry, I haven't learned complex conjugate, and I think my math teacher won't let me use this way, so have other ways to solve?PlzNotation: suppose \(z=a+bi\) then the congregate is \(\overline{~z~}=a-bi\).
Can you show that \((x-z)(x-\overline{~z~})=x^2-2ax+a^2+b^2~?\)
You meant "conjugate", right?Notation: suppose \(z=a+bi\) then the congregate is \(\overline{~z~}=a-bi\).
Can you show that \((x-z)(x-\overline{~z~})=x^2-2ax+a^2+b^2~?\)
One of the ways to do this, w/o using the term (complex conjugate):Given a=3+7i is root of the quadratic equation X^2+px+q=0, where p and q are real numbers.
Question a)Someone claims B=3-7i is also root of the equations.Yes or No ??Explain your answer
Given that 3+ 7i is a root of x^2+ px+q we must have (3+ 7i)^2+ p(3+ 7i)+ q= 9- 49+ 42i+ 3p+ 7p i+ q= (3p+ q- 40)+ (7p+ 42)i= 0. The real and imaginary parts must each be 0 so we have the two equations 3p+ q- 40= 0 and 7p+ 42= 0. Solve the second equation for p and then put that value of p into the first equation to get an equation you can solve for q.Given a=3+7i is root of the quadratic equation X^2+px+q=0, where p and q are real numbers.
Question a)Someone claims B=3-7i is also root of the equations.Yes or No ??Explain your answer
I don't think you've told us yet what you HAVE learned, so all we can do is guess. Please tell us what was taught in the unit associated with this problem.Sorry, I haven't learned complex conjugate, and I think my math teacher won't let me use this way, so have other ways to solve?Plz