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Complex conjugate thingy

Given that 2-4i is a root of the equation
Z^2+pz+q=0

Where p+q are real constants,

(a)Write down the other root of the equation.
2+4i i believe.

(b)Find the value of p and the value of q.
(A=alpha B=beta. Not sure how to get the characters.)
This is where I get a little bit confused. Would you use the equation x^2-(A-B)x+AB
But what is A and what is B in this situation?

Thanks
Original post by Connor_leigh
Given that 2-4i is a root of the equation
Z^2+pz+q=0

Where p+q are real constants,

(a)Write down the other root of the equation.
2+4i i believe.

(b)Find the value of p and the value of q.
(A=alpha B=beta. Not sure how to get the characters.)
This is where I get a little bit confused. Would you use the equation x^2-(A-B)x+AB
But what is A and what is B in this situation?

Thanks


Yes, you would.

Alpha and beta are the roots of the equation.

You can compare the formula to what you've got.
Surely your Alpha and Beta just cancel though and give you a coefficient of 0x?
Original post by Connor_leigh

(A=alpha B=beta. Not sure how to get the characters.)
This is where I get a little bit confused. Would you use the equation x^2-(A-B)x+AB
But what is A and what is B in this situation?

Thanks


Not quite.

If A,B are the two roots, then your quadratic is (x-A)(x-B) giving x2−(A+B)x+ABx^2-(A+B)x+AB

In "A+B", the imaginary parts cancel, but the real parts don't.
Oh it's (A+B). Thanks, I had the equation wrong. :smile:

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